Narrow operators on function spaces and vector lattices /:
"Most classes of operators that are not isomorphic embeddings are characterized by some kind of a "smallness" condition. Narrow operators are those operators defined on function spaces that are "small" at {-1,0,1}-valued functions, e.g. compact operators are narrow. The orig...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Weitere Verfasser: | |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin :
De Gruyter,
[2013]
|
| Schriftenreihe: | De Gruyter studies in mathematics ;
45. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | "Most classes of operators that are not isomorphic embeddings are characterized by some kind of a "smallness" condition. Narrow operators are those operators defined on function spaces that are "small" at {-1,0,1}-valued functions, e.g. compact operators are narrow. The original motivation to consider such operators came from theory of embeddings of Banach spaces, but since then they were also applied to the study of the Daugavet property and to other geometrical problems of functional analysis. The question of when a sum of two narrow operators is narrow, has led to deep developments of the theory of narrow operators, including an extension of the notion to vector lattices and investigations of connections to regular operators. Narrow operators were a subject of numerous investigations during the last 30 years. This monograph provides a comprehensive presentation putting them in context of modern theory. It gives an in depth systematic exposition of concepts related to and influenced by narrow operators, starting from basic results and building up to most recent developments. The authors include a complete bibliography and many attractive open problems."--Publisher's website. |
| Beschreibung: | 1 online resource |
| Bibliographie: | Includes bibliographical references and indexes. |
| ISBN: | 3110263343 9783110263343 |
Internformat
MARC
| LEADER | 00000cam a2200000 i 4500 | ||
|---|---|---|---|
| 001 | ZDB-4-EBA-ocn826444443 | ||
| 003 | OCoLC | ||
| 005 | 20241004212047.0 | ||
| 006 | m o d | ||
| 007 | cr |n||||||||| | ||
| 007 | cr ||||||||||| | ||
| 008 | 130201s2013 gw ob 001 0 eng d | ||
| 010 | |z 2012035986 | ||
| 040 | |a YDXCP |b eng |e pn |c YDXCP |d OCLCO |d N$T |d E7B |d N$T |d IDEBK |d CDX |d OCLCF |d LRU |d EBLCP |d DEBSZ |d OCLCQ |d UAB |d COO |d OCLCQ |d UIU |d AGLDB |d MOR |d PIFAG |d OCLCQ |d MERUC |d OCLCQ |d ZCU |d U3W |d STF |d WRM |d OCLCQ |d VTS |d COCUF |d NRAMU |d ICG |d INT |d VT2 |d OCLCQ |d WYU |d TKN |d OCLCQ |d DKC |d AU@ |d OCLCQ |d AJS |d OCLCO |d OCLCQ |d MUU |d SFB |d VLY |d QGK |d DST |d TNZ |d SHC |d OCLCQ |d OCLCO |d OCLCL |d SXB |d OCLCQ |d OCLCO |d OCLCQ | ||
| 019 | |a 826479699 |a 1131945580 |a 1259130325 | ||
| 020 | |a 3110263343 |q (electronic bk.) | ||
| 020 | |a 9783110263343 |q (electronic bk.) | ||
| 020 | |z 9783110263039 |q (hardcover ; |q alk. paper) | ||
| 020 | |z 3110263033 |q (hardcover ; |q alk. paper) | ||
| 024 | 7 | |a 10.1515/9783110263343 |2 doi | |
| 035 | |a (OCoLC)826444443 |z (OCoLC)826479699 |z (OCoLC)1131945580 |z (OCoLC)1259130325 | ||
| 041 | |a eng | ||
| 050 | 4 | |a QA329.5 |b .P67 2013eb | |
| 072 | 7 | |a MAT |x 031000 |2 bisacsh | |
| 082 | 7 | |a 515/.73 |2 23 | |
| 084 | |a SK 600 |2 rvk |0 (DE-625)rvk/143248: | ||
| 049 | |a MAIN | ||
| 100 | 1 | |a Popov, Mykhaĭlo Mykhaĭlovych, |e author. |1 https://id.oclc.org/worldcat/entity/E39PCjDpHGCY4KvcxpjPGC4xrC |0 http://id.loc.gov/authorities/names/n2012069561 | |
| 245 | 1 | 0 | |a Narrow operators on function spaces and vector lattices / |c by Mikhail Popov, Beata Randrianantoanina. |
| 260 | |a Berlin : |b De Gruyter, |c [2013] | ||
| 300 | |a 1 online resource | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a De Gruyter studies in mathematics ; |v 45 | |
| 504 | |a Includes bibliographical references and indexes. | ||
| 505 | 0 | |a Introduction and preliminaries -- Each "small" operator is narrow -- Applications to nonlocally convex spaces -- Noncompact narrow operators -- Ideal properties, conjugates, spectrum and numerical radii -- Daugavet-type properties of Lebesgue and Lorentz spaces -- Strict singularity versus narrowness -- Weak embeddings of L1 -- Spaces X for which every operator T L(Lp, X) is narrow -- Narrow operators on vector lattices -- Some variants of the notion of narrow operators -- Open problems. | |
| 520 | |a "Most classes of operators that are not isomorphic embeddings are characterized by some kind of a "smallness" condition. Narrow operators are those operators defined on function spaces that are "small" at {-1,0,1}-valued functions, e.g. compact operators are narrow. The original motivation to consider such operators came from theory of embeddings of Banach spaces, but since then they were also applied to the study of the Daugavet property and to other geometrical problems of functional analysis. The question of when a sum of two narrow operators is narrow, has led to deep developments of the theory of narrow operators, including an extension of the notion to vector lattices and investigations of connections to regular operators. Narrow operators were a subject of numerous investigations during the last 30 years. This monograph provides a comprehensive presentation putting them in context of modern theory. It gives an in depth systematic exposition of concepts related to and influenced by narrow operators, starting from basic results and building up to most recent developments. The authors include a complete bibliography and many attractive open problems."--Publisher's website. | ||
| 588 | 0 | |a Description based on online resource; title from digital title page (DeGruyter, viewed September 15, 2023). | |
| 546 | |a In English. | ||
| 650 | 0 | |a Narrow operators. |0 http://id.loc.gov/authorities/subjects/sh2012004275 | |
| 650 | 0 | |a Riesz spaces. |0 http://id.loc.gov/authorities/subjects/sh85114049 | |
| 650 | 0 | |a Function spaces. |0 http://id.loc.gov/authorities/subjects/sh85052310 | |
| 650 | 6 | |a Espaces de Riesz. | |
| 650 | 6 | |a Espaces fonctionnels. | |
| 650 | 7 | |a MATHEMATICS |x Transformations. |2 bisacsh | |
| 650 | 7 | |a Function spaces |2 fast | |
| 650 | 7 | |a Narrow operators |2 fast | |
| 650 | 7 | |a Riesz spaces |2 fast | |
| 653 | |a Function Space. | ||
| 653 | |a Narrow Operator. | ||
| 653 | |a Vector Lattice. | ||
| 700 | 1 | |a Randrianantoanina, Beata. |1 https://id.oclc.org/worldcat/entity/E39PCjDvjQPk6rwycMrV8Kgf4m |0 http://id.loc.gov/authorities/names/n2012069054 | |
| 776 | 0 | 8 | |i Print version: |a Popov, Mykhaĭlo Mykhaĭlovych. |t Narrow operators on function spaces and vector lattices. |d Berlin : De Gruyter, [2013] |z 9783110263039 |w (DLC) 2012035986 |w (OCoLC)818735918 |
| 830 | 0 | |a De Gruyter studies in mathematics ; |v 45. |0 http://id.loc.gov/authorities/names/n83742913 | |
| 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=530546 |3 Volltext |
| 938 | |a Coutts Information Services |b COUT |n 25806458 | ||
| 938 | |a EBL - Ebook Library |b EBLB |n EBL893867 | ||
| 938 | |a ebrary |b EBRY |n ebr10649212 | ||
| 938 | |a EBSCOhost |b EBSC |n 530546 | ||
| 938 | |a ProQuest MyiLibrary Digital eBook Collection |b IDEB |n cis25806458 | ||
| 938 | |a YBP Library Services |b YANK |n 9340288 | ||
| 994 | |a 92 |b GEBAY | ||
| 912 | |a ZDB-4-EBA | ||
| 049 | |a DE-863 | ||
Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn826444443 |
|---|---|
| _version_ | 1816882220634210304 |
| adam_text | |
| any_adam_object | |
| author | Popov, Mykhaĭlo Mykhaĭlovych |
| author2 | Randrianantoanina, Beata |
| author2_role | |
| author2_variant | b r br |
| author_GND | http://id.loc.gov/authorities/names/n2012069561 http://id.loc.gov/authorities/names/n2012069054 |
| author_facet | Popov, Mykhaĭlo Mykhaĭlovych Randrianantoanina, Beata |
| author_role | aut |
| author_sort | Popov, Mykhaĭlo Mykhaĭlovych |
| author_variant | m m p mm mmp |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA329 |
| callnumber-raw | QA329.5 .P67 2013eb |
| callnumber-search | QA329.5 .P67 2013eb |
| callnumber-sort | QA 3329.5 P67 42013EB |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 600 |
| collection | ZDB-4-EBA |
| contents | Introduction and preliminaries -- Each "small" operator is narrow -- Applications to nonlocally convex spaces -- Noncompact narrow operators -- Ideal properties, conjugates, spectrum and numerical radii -- Daugavet-type properties of Lebesgue and Lorentz spaces -- Strict singularity versus narrowness -- Weak embeddings of L1 -- Spaces X for which every operator T L(Lp, X) is narrow -- Narrow operators on vector lattices -- Some variants of the notion of narrow operators -- Open problems. |
| ctrlnum | (OCoLC)826444443 |
| dewey-full | 515/.73 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.73 |
| dewey-search | 515/.73 |
| dewey-sort | 3515 273 |
| 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>05204cam a2200721 i 4500</leader><controlfield tag="001">ZDB-4-EBA-ocn826444443</controlfield><controlfield tag="003">OCoLC</controlfield><controlfield tag="005">20241004212047.0</controlfield><controlfield tag="006">m o d </controlfield><controlfield tag="007">cr |n|||||||||</controlfield><controlfield tag="007">cr |||||||||||</controlfield><controlfield tag="008">130201s2013 gw ob 001 0 eng d</controlfield><datafield tag="010" ind1=" " ind2=" "><subfield code="z"> 2012035986</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">YDXCP</subfield><subfield code="b">eng</subfield><subfield code="e">pn</subfield><subfield code="c">YDXCP</subfield><subfield code="d">OCLCO</subfield><subfield code="d">N$T</subfield><subfield code="d">E7B</subfield><subfield code="d">N$T</subfield><subfield code="d">IDEBK</subfield><subfield code="d">CDX</subfield><subfield code="d">OCLCF</subfield><subfield code="d">LRU</subfield><subfield code="d">EBLCP</subfield><subfield code="d">DEBSZ</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">UAB</subfield><subfield code="d">COO</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">UIU</subfield><subfield code="d">AGLDB</subfield><subfield code="d">MOR</subfield><subfield code="d">PIFAG</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">MERUC</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">ZCU</subfield><subfield code="d">U3W</subfield><subfield code="d">STF</subfield><subfield code="d">WRM</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">VTS</subfield><subfield code="d">COCUF</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">DKC</subfield><subfield code="d">AU@</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">AJS</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">MUU</subfield><subfield code="d">SFB</subfield><subfield code="d">VLY</subfield><subfield code="d">QGK</subfield><subfield code="d">DST</subfield><subfield code="d">TNZ</subfield><subfield code="d">SHC</subfield><subfield code="d">OCLCQ</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">OCLCQ</subfield></datafield><datafield tag="019" ind1=" " ind2=" "><subfield code="a">826479699</subfield><subfield code="a">1131945580</subfield><subfield code="a">1259130325</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3110263343</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783110263343</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">9783110263039</subfield><subfield code="q">(hardcover ;</subfield><subfield code="q">alk. paper)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">3110263033</subfield><subfield code="q">(hardcover ;</subfield><subfield code="q">alk. paper)</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1515/9783110263343</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)826444443</subfield><subfield code="z">(OCoLC)826479699</subfield><subfield code="z">(OCoLC)1131945580</subfield><subfield code="z">(OCoLC)1259130325</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="050" ind1=" " ind2="4"><subfield code="a">QA329.5</subfield><subfield code="b">.P67 2013eb</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">MAT</subfield><subfield code="x">031000</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="082" ind1="7" ind2=" "><subfield code="a">515/.73</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 600</subfield><subfield code="2">rvk</subfield><subfield code="0">(DE-625)rvk/143248:</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">MAIN</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Popov, Mykhaĭlo Mykhaĭlovych,</subfield><subfield code="e">author.</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PCjDpHGCY4KvcxpjPGC4xrC</subfield><subfield code="0">http://id.loc.gov/authorities/names/n2012069561</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Narrow operators on function spaces and vector lattices /</subfield><subfield code="c">by Mikhail Popov, Beata Randrianantoanina.</subfield></datafield><datafield tag="260" ind1=" " ind2=" "><subfield code="a">Berlin :</subfield><subfield code="b">De Gruyter,</subfield><subfield code="c">[2013]</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource</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="490" ind1="1" ind2=" "><subfield code="a">De Gruyter studies in mathematics ;</subfield><subfield code="v">45</subfield></datafield><datafield tag="504" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references and indexes.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">Introduction and preliminaries -- Each "small" operator is narrow -- Applications to nonlocally convex spaces -- Noncompact narrow operators -- Ideal properties, conjugates, spectrum and numerical radii -- Daugavet-type properties of Lebesgue and Lorentz spaces -- Strict singularity versus narrowness -- Weak embeddings of L1 -- Spaces X for which every operator T L(Lp, X) is narrow -- Narrow operators on vector lattices -- Some variants of the notion of narrow operators -- Open problems.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">"Most classes of operators that are not isomorphic embeddings are characterized by some kind of a "smallness" condition. Narrow operators are those operators defined on function spaces that are "small" at {-1,0,1}-valued functions, e.g. compact operators are narrow. The original motivation to consider such operators came from theory of embeddings of Banach spaces, but since then they were also applied to the study of the Daugavet property and to other geometrical problems of functional analysis. The question of when a sum of two narrow operators is narrow, has led to deep developments of the theory of narrow operators, including an extension of the notion to vector lattices and investigations of connections to regular operators. Narrow operators were a subject of numerous investigations during the last 30 years. This monograph provides a comprehensive presentation putting them in context of modern theory. It gives an in depth systematic exposition of concepts related to and influenced by narrow operators, starting from basic results and building up to most recent developments. The authors include a complete bibliography and many attractive open problems."--Publisher's website.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Description based on online resource; title from digital title page (DeGruyter, viewed September 15, 2023).</subfield></datafield><datafield tag="546" ind1=" " ind2=" "><subfield code="a">In English.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Narrow operators.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh2012004275</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Riesz spaces.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85114049</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Function spaces.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85052310</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Espaces de Riesz.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Espaces fonctionnels.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS</subfield><subfield code="x">Transformations.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Function spaces</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Narrow operators</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Riesz spaces</subfield><subfield code="2">fast</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Function Space.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Narrow Operator.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Vector Lattice.</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Randrianantoanina, Beata.</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PCjDvjQPk6rwycMrV8Kgf4m</subfield><subfield code="0">http://id.loc.gov/authorities/names/n2012069054</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Print version:</subfield><subfield code="a">Popov, Mykhaĭlo Mykhaĭlovych.</subfield><subfield code="t">Narrow operators on function spaces and vector lattices.</subfield><subfield code="d">Berlin : De Gruyter, [2013]</subfield><subfield code="z">9783110263039</subfield><subfield code="w">(DLC) 2012035986</subfield><subfield code="w">(OCoLC)818735918</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">De Gruyter studies in mathematics ;</subfield><subfield code="v">45.</subfield><subfield code="0">http://id.loc.gov/authorities/names/n83742913</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=530546</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Coutts Information Services</subfield><subfield code="b">COUT</subfield><subfield code="n">25806458</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBL - Ebook Library</subfield><subfield code="b">EBLB</subfield><subfield code="n">EBL893867</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ebrary</subfield><subfield code="b">EBRY</subfield><subfield code="n">ebr10649212</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBSCOhost</subfield><subfield code="b">EBSC</subfield><subfield code="n">530546</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ProQuest MyiLibrary Digital eBook Collection</subfield><subfield code="b">IDEB</subfield><subfield code="n">cis25806458</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">9340288</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-ocn826444443 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:25:09Z |
| institution | BVB |
| isbn | 3110263343 9783110263343 |
| language | English |
| oclc_num | 826444443 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource |
| psigel | ZDB-4-EBA |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | De Gruyter, |
| record_format | marc |
| series | De Gruyter studies in mathematics ; |
| series2 | De Gruyter studies in mathematics ; |
| spelling | Popov, Mykhaĭlo Mykhaĭlovych, author. https://id.oclc.org/worldcat/entity/E39PCjDpHGCY4KvcxpjPGC4xrC http://id.loc.gov/authorities/names/n2012069561 Narrow operators on function spaces and vector lattices / by Mikhail Popov, Beata Randrianantoanina. Berlin : De Gruyter, [2013] 1 online resource text txt rdacontent computer c rdamedia online resource cr rdacarrier De Gruyter studies in mathematics ; 45 Includes bibliographical references and indexes. Introduction and preliminaries -- Each "small" operator is narrow -- Applications to nonlocally convex spaces -- Noncompact narrow operators -- Ideal properties, conjugates, spectrum and numerical radii -- Daugavet-type properties of Lebesgue and Lorentz spaces -- Strict singularity versus narrowness -- Weak embeddings of L1 -- Spaces X for which every operator T L(Lp, X) is narrow -- Narrow operators on vector lattices -- Some variants of the notion of narrow operators -- Open problems. "Most classes of operators that are not isomorphic embeddings are characterized by some kind of a "smallness" condition. Narrow operators are those operators defined on function spaces that are "small" at {-1,0,1}-valued functions, e.g. compact operators are narrow. The original motivation to consider such operators came from theory of embeddings of Banach spaces, but since then they were also applied to the study of the Daugavet property and to other geometrical problems of functional analysis. The question of when a sum of two narrow operators is narrow, has led to deep developments of the theory of narrow operators, including an extension of the notion to vector lattices and investigations of connections to regular operators. Narrow operators were a subject of numerous investigations during the last 30 years. This monograph provides a comprehensive presentation putting them in context of modern theory. It gives an in depth systematic exposition of concepts related to and influenced by narrow operators, starting from basic results and building up to most recent developments. The authors include a complete bibliography and many attractive open problems."--Publisher's website. Description based on online resource; title from digital title page (DeGruyter, viewed September 15, 2023). In English. Narrow operators. http://id.loc.gov/authorities/subjects/sh2012004275 Riesz spaces. http://id.loc.gov/authorities/subjects/sh85114049 Function spaces. http://id.loc.gov/authorities/subjects/sh85052310 Espaces de Riesz. Espaces fonctionnels. MATHEMATICS Transformations. bisacsh Function spaces fast Narrow operators fast Riesz spaces fast Function Space. Narrow Operator. Vector Lattice. Randrianantoanina, Beata. https://id.oclc.org/worldcat/entity/E39PCjDvjQPk6rwycMrV8Kgf4m http://id.loc.gov/authorities/names/n2012069054 Print version: Popov, Mykhaĭlo Mykhaĭlovych. Narrow operators on function spaces and vector lattices. Berlin : De Gruyter, [2013] 9783110263039 (DLC) 2012035986 (OCoLC)818735918 De Gruyter studies in mathematics ; 45. http://id.loc.gov/authorities/names/n83742913 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=530546 Volltext |
| spellingShingle | Popov, Mykhaĭlo Mykhaĭlovych Narrow operators on function spaces and vector lattices / De Gruyter studies in mathematics ; Introduction and preliminaries -- Each "small" operator is narrow -- Applications to nonlocally convex spaces -- Noncompact narrow operators -- Ideal properties, conjugates, spectrum and numerical radii -- Daugavet-type properties of Lebesgue and Lorentz spaces -- Strict singularity versus narrowness -- Weak embeddings of L1 -- Spaces X for which every operator T L(Lp, X) is narrow -- Narrow operators on vector lattices -- Some variants of the notion of narrow operators -- Open problems. Narrow operators. http://id.loc.gov/authorities/subjects/sh2012004275 Riesz spaces. http://id.loc.gov/authorities/subjects/sh85114049 Function spaces. http://id.loc.gov/authorities/subjects/sh85052310 Espaces de Riesz. Espaces fonctionnels. MATHEMATICS Transformations. bisacsh Function spaces fast Narrow operators fast Riesz spaces fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh2012004275 http://id.loc.gov/authorities/subjects/sh85114049 http://id.loc.gov/authorities/subjects/sh85052310 |
| title | Narrow operators on function spaces and vector lattices / |
| title_auth | Narrow operators on function spaces and vector lattices / |
| title_exact_search | Narrow operators on function spaces and vector lattices / |
| title_full | Narrow operators on function spaces and vector lattices / by Mikhail Popov, Beata Randrianantoanina. |
| title_fullStr | Narrow operators on function spaces and vector lattices / by Mikhail Popov, Beata Randrianantoanina. |
| title_full_unstemmed | Narrow operators on function spaces and vector lattices / by Mikhail Popov, Beata Randrianantoanina. |
| title_short | Narrow operators on function spaces and vector lattices / |
| title_sort | narrow operators on function spaces and vector lattices |
| topic | Narrow operators. http://id.loc.gov/authorities/subjects/sh2012004275 Riesz spaces. http://id.loc.gov/authorities/subjects/sh85114049 Function spaces. http://id.loc.gov/authorities/subjects/sh85052310 Espaces de Riesz. Espaces fonctionnels. MATHEMATICS Transformations. bisacsh Function spaces fast Narrow operators fast Riesz spaces fast |
| topic_facet | Narrow operators. Riesz spaces. Function spaces. Espaces de Riesz. Espaces fonctionnels. MATHEMATICS Transformations. Function spaces Narrow operators Riesz spaces |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=530546 |
| work_keys_str_mv | AT popovmykhailomykhailovych narrowoperatorsonfunctionspacesandvectorlattices AT randrianantoaninabeata narrowoperatorsonfunctionspacesandvectorlattices |