Ultrametric Banach algebras /:
In this volume, ultrametric Banach algebras are studied with the help of topological considerations, properties from affinoid algebra, and circular filters which characterize absolute values on polynomials and make a nice tree structure. The Shilov boundary does exist for normed ultrametric algebras...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore ; River Edge, NJ :
World Scientific,
2003.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | In this volume, ultrametric Banach algebras are studied with the help of topological considerations, properties from affinoid algebra, and circular filters which characterize absolute values on polynomials and make a nice tree structure. The Shilov boundary does exist for normed ultrametric algebras. The spectral norm is equal to the supremum of all continuous multiplicative seminorms whose kernel is a maximal ideal. Two different such seminorms can have the same kernel. Krasner-Tate algebras are characterized among Krasner algebras, affinoid algebra, and ultrametric Banach algebras. Given a Krasner-Tate algbebra A=K{t}[x], the absolute values extending the Gauss norm from K{t} to A are defined by the elements of the Shilov boundary of A. |
| Beschreibung: | 1 online resource (xiii, 275 pages) |
| Bibliographie: | Includes bibliographical references (pages 265-267) and index. |
| ISBN: | 9789812775603 9812775609 1281928267 9781281928269 9786611928261 661192826X |
Internformat
MARC
| LEADER | 00000cam a2200000 a 4500 | ||
|---|---|---|---|
| 001 | ZDB-4-EBA-ocn261483983 | ||
| 003 | OCoLC | ||
| 005 | 20241004212047.0 | ||
| 006 | m o d | ||
| 007 | cr cnu---unuuu | ||
| 008 | 081010s2003 si ob 001 0 eng d | ||
| 040 | |a N$T |b eng |e pn |c N$T |d OCLCQ |d UBY |d IDEBK |d E7B |d OCLCQ |d OCLCF |d OCLCQ |d NLGGC |d YDXCP |d STF |d MHW |d EBLCP |d DEBSZ |d OCLCQ |d AGLDB |d COCUF |d CCO |d PIFAG |d VGM |d ZCU |d OCLCQ |d MERUC |d OCLCQ |d U3W |d WRM |d VTS |d NRAMU |d ICG |d INT |d VT2 |d OCLCQ |d WYU |d TKN |d OCLCQ |d LEAUB |d JBG |d DKC |d OCLCQ |d UKAHL |d OCLCQ |d AJS |d OCLCO |d OCLCQ |d QGK |d OCLCO |d OCLCL |d SXB |d OCLCQ |d OCLCO |d OCLKB | ||
| 019 | |a 505147459 |a 646768176 |a 764498467 |a 815751345 |a 847476067 |a 879025657 |a 961545389 |a 962616460 |a 1259233735 |a 1432916634 | ||
| 020 | |a 9789812775603 |q (electronic bk.) | ||
| 020 | |a 9812775609 |q (electronic bk.) | ||
| 020 | |a 1281928267 | ||
| 020 | |a 9781281928269 | ||
| 020 | |z 9789812381941 | ||
| 020 | |z 9812381945 | ||
| 020 | |a 9786611928261 | ||
| 020 | |a 661192826X | ||
| 035 | |a (OCoLC)261483983 |z (OCoLC)505147459 |z (OCoLC)646768176 |z (OCoLC)764498467 |z (OCoLC)815751345 |z (OCoLC)847476067 |z (OCoLC)879025657 |z (OCoLC)961545389 |z (OCoLC)962616460 |z (OCoLC)1259233735 |z (OCoLC)1432916634 | ||
| 050 | 4 | |a QA326 |b .E8 2003eb | |
| 072 | 7 | |a MAT |x 002050 |2 bisacsh | |
| 072 | 7 | |a PBF |2 bicssc | |
| 082 | 7 | |a 512/.554 |2 22 | |
| 049 | |a MAIN | ||
| 100 | 1 | |a Escassut, Alain. |1 https://id.oclc.org/worldcat/entity/E39PBJqfGXGYYDDK4PHJDf3G73 |0 http://id.loc.gov/authorities/names/nr96008792 | |
| 245 | 1 | 0 | |a Ultrametric Banach algebras / |c Alain Escassut. |
| 260 | |a Singapore ; |a River Edge, NJ : |b World Scientific, |c 2003. | ||
| 300 | |a 1 online resource (xiii, 275 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 504 | |a Includes bibliographical references (pages 265-267) and index. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a In this volume, ultrametric Banach algebras are studied with the help of topological considerations, properties from affinoid algebra, and circular filters which characterize absolute values on polynomials and make a nice tree structure. The Shilov boundary does exist for normed ultrametric algebras. The spectral norm is equal to the supremum of all continuous multiplicative seminorms whose kernel is a maximal ideal. Two different such seminorms can have the same kernel. Krasner-Tate algebras are characterized among Krasner algebras, affinoid algebra, and ultrametric Banach algebras. Given a Krasner-Tate algbebra A=K{t}[x], the absolute values extending the Gauss norm from K{t} to A are defined by the elements of the Shilov boundary of A. | ||
| 505 | 0 | |a 1. Basic properties in commutative algebra -- 2. Tree structure -- 3. Ultrametric absolute values -- 4. L-productal vector spaces -- 5. Multiplicative semi-norms and Shilov boundary -- 6. Spectral semi-norm -- 7. Hensel Lemma -- 8. Infraconnected sets -- 9. Monotonous filters -- 10. Circular filters -- 11. Tree structure and metric on circular filters -- 12. Rational functions and algebras R(D) -- 13. Simple convergence on Mult(K[x]) -- 14. Topologies on Mult(K[x]) -- 15. Spectral properties and Gelfand transforms -- 16. Analytic elements -- 17. Holomorphic properties on infraconnected sets -- 18. T-filters and T-sequences -- 19. Applications of T-filters and T-sequences -- 20. Analytic elements on classic partitions -- 21. Holomorphic properties on partitions -- 22. Shilov boundary for algebras H(D, O) -- 23. Holomorphic functional calculus -- 24. Uniform K-Banach algebras and properties (s) and (q) -- 25. Properties (o) and (q) in uniform Banach K-algebras -- 26. Properties (o) and (q) and strongly valued fields -- 27. Multbijective Banach K-algebras -- 28. Pseudo-density of Mult[symbol] -- 29. Polnorm on algebras and algebraic extensions -- 30. Definition of affinoid algebras -- 31. Algebraic properties of affinoid algebras -- 32. Jacobson radical of affinoid algebras -- 33. Salmon's theorems -- 34. Separable fields -- 35. Spectral norm of affinoid algebras -- 36. Spectrum of an element of an affinoid algebra -- 37. Krasner-Tate algebras -- 38. Universal generators in Tate algebras -- 39. Mappings from H(D) to the tree Mult(K[x]) -- 40. Continuous mappings on Mult(K[x]) -- 41. Examples and counterexamples -- 41. Associated idempotents -- 43. Krasner-Tate algebras among Banach K-algebras. | |
| 546 | |a English. | ||
| 650 | 0 | |a Banach algebras. |0 http://id.loc.gov/authorities/subjects/sh85011437 | |
| 650 | 7 | |a MATHEMATICS |x Algebra |x Linear. |2 bisacsh | |
| 650 | 7 | |a Banach algebras |2 fast | |
| 650 | 1 | 7 | |a Algèbre de Banach. |2 rasuqam |
| 650 | 7 | |a Analyse p-adique. |2 rasuqam | |
| 758 | |i has work: |a Ultrametric Banach algebras (Text) |1 https://id.oclc.org/worldcat/entity/E39PCH4Bj4d8WdxyK7mMjB7dkP |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Escassut, Alain. |t Ultrametric Banach algebras. |d Singapore ; River Edge, NJ : World Scientific, 2003 |z 9812381945 |z 9789812381941 |w (OCoLC)52425467 |
| 856 | 4 | 0 | |l FWS01 |p ZDB-4-EBA |q FWS_PDA_EBA |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235727 |3 Volltext |
| 938 | |a Askews and Holts Library Services |b ASKH |n AH24684598 | ||
| 938 | |a EBL - Ebook Library |b EBLB |n EBL1681773 | ||
| 938 | |a ebrary |b EBRY |n ebr10255411 | ||
| 938 | |a EBSCOhost |b EBSC |n 235727 | ||
| 938 | |a ProQuest MyiLibrary Digital eBook Collection |b IDEB |n 192826 | ||
| 938 | |a YBP Library Services |b YANK |n 2889225 | ||
| 938 | |b OCKB |z perlego.catalogue,d699dd60-35c0-4135-a29f-a62dad35ff38-emi | ||
| 994 | |a 92 |b GEBAY | ||
| 912 | |a ZDB-4-EBA | ||
| 049 | |a DE-863 | ||
Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn261483983 |
|---|---|
| _version_ | 1816881678788853760 |
| adam_text | |
| any_adam_object | |
| author | Escassut, Alain |
| author_GND | http://id.loc.gov/authorities/names/nr96008792 |
| author_facet | Escassut, Alain |
| author_role | |
| author_sort | Escassut, Alain |
| author_variant | a e ae |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA326 |
| callnumber-raw | QA326 .E8 2003eb |
| callnumber-search | QA326 .E8 2003eb |
| callnumber-sort | QA 3326 E8 42003EB |
| callnumber-subject | QA - Mathematics |
| collection | ZDB-4-EBA |
| contents | 1. Basic properties in commutative algebra -- 2. Tree structure -- 3. Ultrametric absolute values -- 4. L-productal vector spaces -- 5. Multiplicative semi-norms and Shilov boundary -- 6. Spectral semi-norm -- 7. Hensel Lemma -- 8. Infraconnected sets -- 9. Monotonous filters -- 10. Circular filters -- 11. Tree structure and metric on circular filters -- 12. Rational functions and algebras R(D) -- 13. Simple convergence on Mult(K[x]) -- 14. Topologies on Mult(K[x]) -- 15. Spectral properties and Gelfand transforms -- 16. Analytic elements -- 17. Holomorphic properties on infraconnected sets -- 18. T-filters and T-sequences -- 19. Applications of T-filters and T-sequences -- 20. Analytic elements on classic partitions -- 21. Holomorphic properties on partitions -- 22. Shilov boundary for algebras H(D, O) -- 23. Holomorphic functional calculus -- 24. Uniform K-Banach algebras and properties (s) and (q) -- 25. Properties (o) and (q) in uniform Banach K-algebras -- 26. Properties (o) and (q) and strongly valued fields -- 27. Multbijective Banach K-algebras -- 28. Pseudo-density of Mult[symbol] -- 29. Polnorm on algebras and algebraic extensions -- 30. Definition of affinoid algebras -- 31. Algebraic properties of affinoid algebras -- 32. Jacobson radical of affinoid algebras -- 33. Salmon's theorems -- 34. Separable fields -- 35. Spectral norm of affinoid algebras -- 36. Spectrum of an element of an affinoid algebra -- 37. Krasner-Tate algebras -- 38. Universal generators in Tate algebras -- 39. Mappings from H(D) to the tree Mult(K[x]) -- 40. Continuous mappings on Mult(K[x]) -- 41. Examples and counterexamples -- 41. Associated idempotents -- 43. Krasner-Tate algebras among Banach K-algebras. |
| ctrlnum | (OCoLC)261483983 |
| dewey-full | 512/.554 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.554 |
| dewey-search | 512/.554 |
| dewey-sort | 3512 3554 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>05558cam a2200625 a 4500</leader><controlfield tag="001">ZDB-4-EBA-ocn261483983</controlfield><controlfield tag="003">OCoLC</controlfield><controlfield tag="005">20241004212047.0</controlfield><controlfield tag="006">m o d </controlfield><controlfield tag="007">cr cnu---unuuu</controlfield><controlfield tag="008">081010s2003 si ob 001 0 eng d</controlfield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">N$T</subfield><subfield code="b">eng</subfield><subfield code="e">pn</subfield><subfield code="c">N$T</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">UBY</subfield><subfield code="d">IDEBK</subfield><subfield code="d">E7B</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCF</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">NLGGC</subfield><subfield code="d">YDXCP</subfield><subfield code="d">STF</subfield><subfield code="d">MHW</subfield><subfield code="d">EBLCP</subfield><subfield code="d">DEBSZ</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">AGLDB</subfield><subfield code="d">COCUF</subfield><subfield code="d">CCO</subfield><subfield code="d">PIFAG</subfield><subfield code="d">VGM</subfield><subfield code="d">ZCU</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">MERUC</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">U3W</subfield><subfield code="d">WRM</subfield><subfield code="d">VTS</subfield><subfield code="d">NRAMU</subfield><subfield code="d">ICG</subfield><subfield code="d">INT</subfield><subfield code="d">VT2</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">WYU</subfield><subfield code="d">TKN</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">LEAUB</subfield><subfield code="d">JBG</subfield><subfield code="d">DKC</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">UKAHL</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">AJS</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">QGK</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCL</subfield><subfield code="d">SXB</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLKB</subfield></datafield><datafield tag="019" ind1=" " ind2=" "><subfield code="a">505147459</subfield><subfield code="a">646768176</subfield><subfield code="a">764498467</subfield><subfield code="a">815751345</subfield><subfield code="a">847476067</subfield><subfield code="a">879025657</subfield><subfield code="a">961545389</subfield><subfield code="a">962616460</subfield><subfield code="a">1259233735</subfield><subfield code="a">1432916634</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789812775603</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9812775609</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1281928267</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781281928269</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">9789812381941</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">9812381945</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9786611928261</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">661192826X</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)261483983</subfield><subfield code="z">(OCoLC)505147459</subfield><subfield code="z">(OCoLC)646768176</subfield><subfield code="z">(OCoLC)764498467</subfield><subfield code="z">(OCoLC)815751345</subfield><subfield code="z">(OCoLC)847476067</subfield><subfield code="z">(OCoLC)879025657</subfield><subfield code="z">(OCoLC)961545389</subfield><subfield code="z">(OCoLC)962616460</subfield><subfield code="z">(OCoLC)1259233735</subfield><subfield code="z">(OCoLC)1432916634</subfield></datafield><datafield tag="050" ind1=" " ind2="4"><subfield code="a">QA326</subfield><subfield code="b">.E8 2003eb</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">MAT</subfield><subfield code="x">002050</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">PBF</subfield><subfield code="2">bicssc</subfield></datafield><datafield tag="082" ind1="7" ind2=" "><subfield code="a">512/.554</subfield><subfield code="2">22</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">MAIN</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Escassut, Alain.</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PBJqfGXGYYDDK4PHJDf3G73</subfield><subfield code="0">http://id.loc.gov/authorities/names/nr96008792</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Ultrametric Banach algebras /</subfield><subfield code="c">Alain Escassut.</subfield></datafield><datafield tag="260" ind1=" " ind2=" "><subfield code="a">Singapore ;</subfield><subfield code="a">River Edge, NJ :</subfield><subfield code="b">World Scientific,</subfield><subfield code="c">2003.</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (xiii, 275 pages)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="504" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references (pages 265-267) and index.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Print version record.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">In this volume, ultrametric Banach algebras are studied with the help of topological considerations, properties from affinoid algebra, and circular filters which characterize absolute values on polynomials and make a nice tree structure. The Shilov boundary does exist for normed ultrametric algebras. The spectral norm is equal to the supremum of all continuous multiplicative seminorms whose kernel is a maximal ideal. Two different such seminorms can have the same kernel. Krasner-Tate algebras are characterized among Krasner algebras, affinoid algebra, and ultrametric Banach algebras. Given a Krasner-Tate algbebra A=K{t}[x], the absolute values extending the Gauss norm from K{t} to A are defined by the elements of the Shilov boundary of A.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">1. Basic properties in commutative algebra -- 2. Tree structure -- 3. Ultrametric absolute values -- 4. L-productal vector spaces -- 5. Multiplicative semi-norms and Shilov boundary -- 6. Spectral semi-norm -- 7. Hensel Lemma -- 8. Infraconnected sets -- 9. Monotonous filters -- 10. Circular filters -- 11. Tree structure and metric on circular filters -- 12. Rational functions and algebras R(D) -- 13. Simple convergence on Mult(K[x]) -- 14. Topologies on Mult(K[x]) -- 15. Spectral properties and Gelfand transforms -- 16. Analytic elements -- 17. Holomorphic properties on infraconnected sets -- 18. T-filters and T-sequences -- 19. Applications of T-filters and T-sequences -- 20. Analytic elements on classic partitions -- 21. Holomorphic properties on partitions -- 22. Shilov boundary for algebras H(D, O) -- 23. Holomorphic functional calculus -- 24. Uniform K-Banach algebras and properties (s) and (q) -- 25. Properties (o) and (q) in uniform Banach K-algebras -- 26. Properties (o) and (q) and strongly valued fields -- 27. Multbijective Banach K-algebras -- 28. Pseudo-density of Mult[symbol] -- 29. Polnorm on algebras and algebraic extensions -- 30. Definition of affinoid algebras -- 31. Algebraic properties of affinoid algebras -- 32. Jacobson radical of affinoid algebras -- 33. Salmon's theorems -- 34. Separable fields -- 35. Spectral norm of affinoid algebras -- 36. Spectrum of an element of an affinoid algebra -- 37. Krasner-Tate algebras -- 38. Universal generators in Tate algebras -- 39. Mappings from H(D) to the tree Mult(K[x]) -- 40. Continuous mappings on Mult(K[x]) -- 41. Examples and counterexamples -- 41. Associated idempotents -- 43. Krasner-Tate algebras among Banach K-algebras.</subfield></datafield><datafield tag="546" ind1=" " ind2=" "><subfield code="a">English.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Banach algebras.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85011437</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS</subfield><subfield code="x">Algebra</subfield><subfield code="x">Linear.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Banach algebras</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1="1" ind2="7"><subfield code="a">Algèbre de Banach.</subfield><subfield code="2">rasuqam</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Analyse p-adique.</subfield><subfield code="2">rasuqam</subfield></datafield><datafield tag="758" ind1=" " ind2=" "><subfield code="i">has work:</subfield><subfield code="a">Ultrametric Banach algebras (Text)</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PCH4Bj4d8WdxyK7mMjB7dkP</subfield><subfield code="4">https://id.oclc.org/worldcat/ontology/hasWork</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Print version:</subfield><subfield code="a">Escassut, Alain.</subfield><subfield code="t">Ultrametric Banach algebras.</subfield><subfield code="d">Singapore ; River Edge, NJ : World Scientific, 2003</subfield><subfield code="z">9812381945</subfield><subfield code="z">9789812381941</subfield><subfield code="w">(OCoLC)52425467</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="l">FWS01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235727</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Askews and Holts Library Services</subfield><subfield code="b">ASKH</subfield><subfield code="n">AH24684598</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBL - Ebook Library</subfield><subfield code="b">EBLB</subfield><subfield code="n">EBL1681773</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ebrary</subfield><subfield code="b">EBRY</subfield><subfield code="n">ebr10255411</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBSCOhost</subfield><subfield code="b">EBSC</subfield><subfield code="n">235727</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ProQuest MyiLibrary Digital eBook Collection</subfield><subfield code="b">IDEB</subfield><subfield code="n">192826</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">2889225</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="b">OCKB</subfield><subfield code="z">perlego.catalogue,d699dd60-35c0-4135-a29f-a62dad35ff38-emi</subfield></datafield><datafield tag="994" ind1=" " ind2=" "><subfield code="a">92</subfield><subfield code="b">GEBAY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-4-EBA</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-863</subfield></datafield></record></collection> |
| id | ZDB-4-EBA-ocn261483983 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:16:32Z |
| institution | BVB |
| isbn | 9789812775603 9812775609 1281928267 9781281928269 9786611928261 661192826X |
| language | English |
| oclc_num | 261483983 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xiii, 275 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | World Scientific, |
| record_format | marc |
| spelling | Escassut, Alain. https://id.oclc.org/worldcat/entity/E39PBJqfGXGYYDDK4PHJDf3G73 http://id.loc.gov/authorities/names/nr96008792 Ultrametric Banach algebras / Alain Escassut. Singapore ; River Edge, NJ : World Scientific, 2003. 1 online resource (xiii, 275 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Includes bibliographical references (pages 265-267) and index. Print version record. In this volume, ultrametric Banach algebras are studied with the help of topological considerations, properties from affinoid algebra, and circular filters which characterize absolute values on polynomials and make a nice tree structure. The Shilov boundary does exist for normed ultrametric algebras. The spectral norm is equal to the supremum of all continuous multiplicative seminorms whose kernel is a maximal ideal. Two different such seminorms can have the same kernel. Krasner-Tate algebras are characterized among Krasner algebras, affinoid algebra, and ultrametric Banach algebras. Given a Krasner-Tate algbebra A=K{t}[x], the absolute values extending the Gauss norm from K{t} to A are defined by the elements of the Shilov boundary of A. 1. Basic properties in commutative algebra -- 2. Tree structure -- 3. Ultrametric absolute values -- 4. L-productal vector spaces -- 5. Multiplicative semi-norms and Shilov boundary -- 6. Spectral semi-norm -- 7. Hensel Lemma -- 8. Infraconnected sets -- 9. Monotonous filters -- 10. Circular filters -- 11. Tree structure and metric on circular filters -- 12. Rational functions and algebras R(D) -- 13. Simple convergence on Mult(K[x]) -- 14. Topologies on Mult(K[x]) -- 15. Spectral properties and Gelfand transforms -- 16. Analytic elements -- 17. Holomorphic properties on infraconnected sets -- 18. T-filters and T-sequences -- 19. Applications of T-filters and T-sequences -- 20. Analytic elements on classic partitions -- 21. Holomorphic properties on partitions -- 22. Shilov boundary for algebras H(D, O) -- 23. Holomorphic functional calculus -- 24. Uniform K-Banach algebras and properties (s) and (q) -- 25. Properties (o) and (q) in uniform Banach K-algebras -- 26. Properties (o) and (q) and strongly valued fields -- 27. Multbijective Banach K-algebras -- 28. Pseudo-density of Mult[symbol] -- 29. Polnorm on algebras and algebraic extensions -- 30. Definition of affinoid algebras -- 31. Algebraic properties of affinoid algebras -- 32. Jacobson radical of affinoid algebras -- 33. Salmon's theorems -- 34. Separable fields -- 35. Spectral norm of affinoid algebras -- 36. Spectrum of an element of an affinoid algebra -- 37. Krasner-Tate algebras -- 38. Universal generators in Tate algebras -- 39. Mappings from H(D) to the tree Mult(K[x]) -- 40. Continuous mappings on Mult(K[x]) -- 41. Examples and counterexamples -- 41. Associated idempotents -- 43. Krasner-Tate algebras among Banach K-algebras. English. Banach algebras. http://id.loc.gov/authorities/subjects/sh85011437 MATHEMATICS Algebra Linear. bisacsh Banach algebras fast Algèbre de Banach. rasuqam Analyse p-adique. rasuqam has work: Ultrametric Banach algebras (Text) https://id.oclc.org/worldcat/entity/E39PCH4Bj4d8WdxyK7mMjB7dkP https://id.oclc.org/worldcat/ontology/hasWork Print version: Escassut, Alain. Ultrametric Banach algebras. Singapore ; River Edge, NJ : World Scientific, 2003 9812381945 9789812381941 (OCoLC)52425467 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235727 Volltext |
| spellingShingle | Escassut, Alain Ultrametric Banach algebras / 1. Basic properties in commutative algebra -- 2. Tree structure -- 3. Ultrametric absolute values -- 4. L-productal vector spaces -- 5. Multiplicative semi-norms and Shilov boundary -- 6. Spectral semi-norm -- 7. Hensel Lemma -- 8. Infraconnected sets -- 9. Monotonous filters -- 10. Circular filters -- 11. Tree structure and metric on circular filters -- 12. Rational functions and algebras R(D) -- 13. Simple convergence on Mult(K[x]) -- 14. Topologies on Mult(K[x]) -- 15. Spectral properties and Gelfand transforms -- 16. Analytic elements -- 17. Holomorphic properties on infraconnected sets -- 18. T-filters and T-sequences -- 19. Applications of T-filters and T-sequences -- 20. Analytic elements on classic partitions -- 21. Holomorphic properties on partitions -- 22. Shilov boundary for algebras H(D, O) -- 23. Holomorphic functional calculus -- 24. Uniform K-Banach algebras and properties (s) and (q) -- 25. Properties (o) and (q) in uniform Banach K-algebras -- 26. Properties (o) and (q) and strongly valued fields -- 27. Multbijective Banach K-algebras -- 28. Pseudo-density of Mult[symbol] -- 29. Polnorm on algebras and algebraic extensions -- 30. Definition of affinoid algebras -- 31. Algebraic properties of affinoid algebras -- 32. Jacobson radical of affinoid algebras -- 33. Salmon's theorems -- 34. Separable fields -- 35. Spectral norm of affinoid algebras -- 36. Spectrum of an element of an affinoid algebra -- 37. Krasner-Tate algebras -- 38. Universal generators in Tate algebras -- 39. Mappings from H(D) to the tree Mult(K[x]) -- 40. Continuous mappings on Mult(K[x]) -- 41. Examples and counterexamples -- 41. Associated idempotents -- 43. Krasner-Tate algebras among Banach K-algebras. Banach algebras. http://id.loc.gov/authorities/subjects/sh85011437 MATHEMATICS Algebra Linear. bisacsh Banach algebras fast Algèbre de Banach. rasuqam Analyse p-adique. rasuqam |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85011437 |
| title | Ultrametric Banach algebras / |
| title_auth | Ultrametric Banach algebras / |
| title_exact_search | Ultrametric Banach algebras / |
| title_full | Ultrametric Banach algebras / Alain Escassut. |
| title_fullStr | Ultrametric Banach algebras / Alain Escassut. |
| title_full_unstemmed | Ultrametric Banach algebras / Alain Escassut. |
| title_short | Ultrametric Banach algebras / |
| title_sort | ultrametric banach algebras |
| topic | Banach algebras. http://id.loc.gov/authorities/subjects/sh85011437 MATHEMATICS Algebra Linear. bisacsh Banach algebras fast Algèbre de Banach. rasuqam Analyse p-adique. rasuqam |
| topic_facet | Banach algebras. MATHEMATICS Algebra Linear. Banach algebras Algèbre de Banach. Analyse p-adique. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235727 |
| work_keys_str_mv | AT escassutalain ultrametricbanachalgebras |