Local Multipliers of C*-Algebras:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
London
Springer London
2003
|
| Series: | Springer Monographs in Mathematics
|
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | Many problems in operator theory lead to the consideration ofoperator equations, either directly or via some reformulation. More often than not, however, the underlying space is too 'small' to contain solutions of these equations and thus it has to be 'enlarged' in some way. The Berberian-Quigley enlargement of a Banach space, which allows one to convert approximate into genuine eigenvectors, serves as a classical example. In the theory of operator algebras, a C*-algebra A that turns out to be small in this sense traditionally is enlarged to its (universal) enveloping von Neumann algebra A". This works well since von Neumann algebras are in many respects richer and, from the Banach space point of view, A" is nothing other than the second dual space of A. Among the numerous fruitful applications of this principle is the well-known Kadison-Sakai theorem ensuring that every derivation 8 on a C*-algebra A becomes inner in A", though 8 may not be inner in A. The transition from A to A" however is not an algebraic one (and cannot be since it is well known that the property of being a von Neumann algebra cannot be described purely algebraically). Hence, if the C*-algebra A is small in an algebraic sense, say simple, it may be inappropriate to move on to A". In such a situation, A is typically enlarged by its multiplier algebra M(A) |
| Physical Description: | 1 Online-Ressource (XII, 319 p) |
| ISBN: | 9781447100454 9781447110682 |
| ISSN: | 1439-7382 |
| DOI: | 10.1007/978-1-4471-0045-4 |
Staff View
MARC
| LEADER | 00000nmm a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV042419338 | ||
| 003 | DE-604 | ||
| 005 | 20180115 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s2003 |||| o||u| ||||||eng d | ||
| 020 | |a 9781447100454 |c Online |9 978-1-4471-0045-4 | ||
| 020 | |a 9781447110682 |c Print |9 978-1-4471-1068-2 | ||
| 024 | 7 | |a 10.1007/978-1-4471-0045-4 |2 doi | |
| 035 | |a (OCoLC)869859854 | ||
| 035 | |a (DE-599)BVBBV042419338 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 512 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Ara, Pere |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Local Multipliers of C*-Algebras |c by Pere Ara, Martin Mathieu |
| 264 | 1 | |a London |b Springer London |c 2003 | |
| 300 | |a 1 Online-Ressource (XII, 319 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Springer Monographs in Mathematics |x 1439-7382 | |
| 500 | |a Many problems in operator theory lead to the consideration ofoperator equations, either directly or via some reformulation. More often than not, however, the underlying space is too 'small' to contain solutions of these equations and thus it has to be 'enlarged' in some way. The Berberian-Quigley enlargement of a Banach space, which allows one to convert approximate into genuine eigenvectors, serves as a classical example. In the theory of operator algebras, a C*-algebra A that turns out to be small in this sense traditionally is enlarged to its (universal) enveloping von Neumann algebra A". This works well since von Neumann algebras are in many respects richer and, from the Banach space point of view, A" is nothing other than the second dual space of A. Among the numerous fruitful applications of this principle is the well-known Kadison-Sakai theorem ensuring that every derivation 8 on a C*-algebra A becomes inner in A", though 8 may not be inner in A. The transition from A to A" however is not an algebraic one (and cannot be since it is well known that the property of being a von Neumann algebra cannot be described purely algebraically). Hence, if the C*-algebra A is small in an algebraic sense, say simple, it may be inappropriate to move on to A". In such a situation, A is typically enlarged by its multiplier algebra M(A) | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Algebra | |
| 650 | 4 | |a Functional analysis | |
| 650 | 4 | |a Operator theory | |
| 650 | 4 | |a Operator Theory | |
| 650 | 4 | |a Functional Analysis | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Multiplikator |0 (DE-588)4040703-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a C-Stern-Algebra |0 (DE-588)4136693-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a C-Stern-Algebra |0 (DE-588)4136693-1 |D s |
| 689 | 0 | 1 | |a Multiplikator |0 (DE-588)4040703-2 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 700 | 1 | |a Mathieu, Martin |e Sonstige |4 oth | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-1-4471-0045-4 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027854755 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Record in the Search Index
| _version_ | 1804153089858469888 |
|---|---|
| any_adam_object | |
| author | Ara, Pere |
| author_facet | Ara, Pere |
| author_role | aut |
| author_sort | Ara, Pere |
| author_variant | p a pa |
| building | Verbundindex |
| bvnumber | BV042419338 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)869859854 (DE-599)BVBBV042419338 |
| dewey-full | 512 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512 |
| dewey-search | 512 |
| dewey-sort | 3512 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4471-0045-4 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03106nmm a2200529zc 4500</leader><controlfield tag="001">BV042419338</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20180115 </controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s2003 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781447100454</subfield><subfield code="c">Online</subfield><subfield code="9">978-1-4471-0045-4</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781447110682</subfield><subfield code="c">Print</subfield><subfield code="9">978-1-4471-1068-2</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-1-4471-0045-4</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)869859854</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042419338</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Ara, Pere</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Local Multipliers of C*-Algebras</subfield><subfield code="c">by Pere Ara, Martin Mathieu</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">London</subfield><subfield code="b">Springer London</subfield><subfield code="c">2003</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (XII, 319 p)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Springer Monographs in Mathematics</subfield><subfield code="x">1439-7382</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Many problems in operator theory lead to the consideration ofoperator equations, either directly or via some reformulation. More often than not, however, the underlying space is too 'small' to contain solutions of these equations and thus it has to be 'enlarged' in some way. The Berberian-Quigley enlargement of a Banach space, which allows one to convert approximate into genuine eigenvectors, serves as a classical example. In the theory of operator algebras, a C*-algebra A that turns out to be small in this sense traditionally is enlarged to its (universal) enveloping von Neumann algebra A". This works well since von Neumann algebras are in many respects richer and, from the Banach space point of view, A" is nothing other than the second dual space of A. Among the numerous fruitful applications of this principle is the well-known Kadison-Sakai theorem ensuring that every derivation 8 on a C*-algebra A becomes inner in A", though 8 may not be inner in A. The transition from A to A" however is not an algebraic one (and cannot be since it is well known that the property of being a von Neumann algebra cannot be described purely algebraically). Hence, if the C*-algebra A is small in an algebraic sense, say simple, it may be inappropriate to move on to A". In such a situation, A is typically enlarged by its multiplier algebra M(A)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Algebra</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Functional analysis</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Operator theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Operator Theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Functional Analysis</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Multiplikator</subfield><subfield code="0">(DE-588)4040703-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">C-Stern-Algebra</subfield><subfield code="0">(DE-588)4136693-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">C-Stern-Algebra</subfield><subfield code="0">(DE-588)4136693-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Multiplikator</subfield><subfield code="0">(DE-588)4040703-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Mathieu, Martin</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-1-4471-0045-4</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027854755</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| id | DE-604.BV042419338 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:04Z |
| institution | BVB |
| isbn | 9781447100454 9781447110682 |
| issn | 1439-7382 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027854755 |
| oclc_num | 869859854 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (XII, 319 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Springer London |
| record_format | marc |
| series2 | Springer Monographs in Mathematics |
| spelling | Ara, Pere Verfasser aut Local Multipliers of C*-Algebras by Pere Ara, Martin Mathieu London Springer London 2003 1 Online-Ressource (XII, 319 p) txt rdacontent c rdamedia cr rdacarrier Springer Monographs in Mathematics 1439-7382 Many problems in operator theory lead to the consideration ofoperator equations, either directly or via some reformulation. More often than not, however, the underlying space is too 'small' to contain solutions of these equations and thus it has to be 'enlarged' in some way. The Berberian-Quigley enlargement of a Banach space, which allows one to convert approximate into genuine eigenvectors, serves as a classical example. In the theory of operator algebras, a C*-algebra A that turns out to be small in this sense traditionally is enlarged to its (universal) enveloping von Neumann algebra A". This works well since von Neumann algebras are in many respects richer and, from the Banach space point of view, A" is nothing other than the second dual space of A. Among the numerous fruitful applications of this principle is the well-known Kadison-Sakai theorem ensuring that every derivation 8 on a C*-algebra A becomes inner in A", though 8 may not be inner in A. The transition from A to A" however is not an algebraic one (and cannot be since it is well known that the property of being a von Neumann algebra cannot be described purely algebraically). Hence, if the C*-algebra A is small in an algebraic sense, say simple, it may be inappropriate to move on to A". In such a situation, A is typically enlarged by its multiplier algebra M(A) Mathematics Algebra Functional analysis Operator theory Operator Theory Functional Analysis Mathematik Multiplikator (DE-588)4040703-2 gnd rswk-swf C-Stern-Algebra (DE-588)4136693-1 gnd rswk-swf C-Stern-Algebra (DE-588)4136693-1 s Multiplikator (DE-588)4040703-2 s 1\p DE-604 Mathieu, Martin Sonstige oth https://doi.org/10.1007/978-1-4471-0045-4 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Ara, Pere Local Multipliers of C*-Algebras Mathematics Algebra Functional analysis Operator theory Operator Theory Functional Analysis Mathematik Multiplikator (DE-588)4040703-2 gnd C-Stern-Algebra (DE-588)4136693-1 gnd |
| subject_GND | (DE-588)4040703-2 (DE-588)4136693-1 |
| title | Local Multipliers of C*-Algebras |
| title_auth | Local Multipliers of C*-Algebras |
| title_exact_search | Local Multipliers of C*-Algebras |
| title_full | Local Multipliers of C*-Algebras by Pere Ara, Martin Mathieu |
| title_fullStr | Local Multipliers of C*-Algebras by Pere Ara, Martin Mathieu |
| title_full_unstemmed | Local Multipliers of C*-Algebras by Pere Ara, Martin Mathieu |
| title_short | Local Multipliers of C*-Algebras |
| title_sort | local multipliers of c algebras |
| topic | Mathematics Algebra Functional analysis Operator theory Operator Theory Functional Analysis Mathematik Multiplikator (DE-588)4040703-2 gnd C-Stern-Algebra (DE-588)4136693-1 gnd |
| topic_facet | Mathematics Algebra Functional analysis Operator theory Operator Theory Functional Analysis Mathematik Multiplikator C-Stern-Algebra |
| url | https://doi.org/10.1007/978-1-4471-0045-4 |
| work_keys_str_mv | AT arapere localmultipliersofcalgebras AT mathieumartin localmultipliersofcalgebras |