Narrow operators on function spaces and vector lattices:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin
De Gruyter
c2013
|
| Series: | De Gruyter studies in mathematics
45 |
| Subjects: | |
| Online Access: | FAW01 FAW02 Volltext |
| Item Description: | Description based on print version record |
| Physical Description: | 1 online resource (xiii, 319 p.) |
| ISBN: | 3110263343 9783110263343 |
Staff View
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| 245 | 1 | 0 | |a Narrow operators on function spaces and vector lattices |c by Mikhail Popov, Beata Randrianantoanina |
| 264 | 1 | |a Berlin |b De Gruyter |c c2013 | |
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| 505 | 8 | |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 | |
| 505 | 8 | |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 | |
| 650 | 7 | |a MATHEMATICS / Transformations |2 bisacsh | |
| 650 | 7 | |a Function spaces |2 fast | |
| 650 | 7 | |a Narrow operators |2 fast | |
| 650 | 7 | |a Riesz spaces |2 fast | |
| 650 | 4 | |a Narrow operators | |
| 650 | 4 | |a Riesz spaces | |
| 650 | 4 | |a Function spaces | |
| 650 | 0 | 7 | |a Operator |0 (DE-588)4130529-2 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Randrianantoanina, Beata |e Sonstige |4 oth | |
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Record in the Search Index
| _version_ | 1804175401813016576 |
|---|---|
| any_adam_object | |
| author | Popov, Mykhaĭlo Mykhaĭlovych |
| author_facet | Popov, Mykhaĭlo Mykhaĭlovych |
| author_role | aut |
| author_sort | Popov, Mykhaĭlo Mykhaĭlovych |
| author_variant | m m p mm mmp |
| building | Verbundindex |
| bvnumber | BV043039271 |
| classification_rvk | SK 620 |
| 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 "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 |
| ctrlnum | (OCoLC)826444443 (DE-599)BVBBV043039271 |
| 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 |
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| id | DE-604.BV043039271 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:15:42Z |
| institution | BVB |
| isbn | 3110263343 9783110263343 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028463917 |
| oclc_num | 826444443 |
| open_access_boolean | |
| owner | DE-1046 DE-1047 |
| owner_facet | DE-1046 DE-1047 |
| physical | 1 online resource (xiii, 319 p.) |
| psigel | ZDB-4-EBA ZDB-4-EBA FAW_PDA_EBA |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | De Gruyter |
| record_format | marc |
| series2 | De Gruyter studies in mathematics |
| spelling | Popov, Mykhaĭlo Mykhaĭlovych Verfasser aut Narrow operators on function spaces and vector lattices by Mikhail Popov, Beata Randrianantoanina Berlin De Gruyter c2013 1 online resource (xiii, 319 p.) txt rdacontent c rdamedia cr rdacarrier De Gruyter studies in mathematics 45 Description based on print version record 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 MATHEMATICS / Transformations bisacsh Function spaces fast Narrow operators fast Riesz spaces fast Narrow operators Riesz spaces Function spaces Operator (DE-588)4130529-2 gnd rswk-swf Vektorverband (DE-588)4187471-7 gnd rswk-swf Funktionenraum (DE-588)4134834-5 gnd rswk-swf Operator (DE-588)4130529-2 s Funktionenraum (DE-588)4134834-5 s Vektorverband (DE-588)4187471-7 s 1\p DE-604 Randrianantoanina, Beata Sonstige oth Erscheint auch als Druck-Ausgabe Popov, Mykhaĭlo Mykhaĭlovych Narrow operators on function spaces and vector lattices Erscheint auch als Druckausgabe 3-11-026303-3 Erscheint auch als Druckausgabe 978-3-11-026303-9 http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=530546 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Popov, Mykhaĭlo Mykhaĭlovych Narrow operators on function spaces and vector lattices 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 MATHEMATICS / Transformations bisacsh Function spaces fast Narrow operators fast Riesz spaces fast Narrow operators Riesz spaces Function spaces Operator (DE-588)4130529-2 gnd Vektorverband (DE-588)4187471-7 gnd Funktionenraum (DE-588)4134834-5 gnd |
| subject_GND | (DE-588)4130529-2 (DE-588)4187471-7 (DE-588)4134834-5 |
| 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 | MATHEMATICS / Transformations bisacsh Function spaces fast Narrow operators fast Riesz spaces fast Narrow operators Riesz spaces Function spaces Operator (DE-588)4130529-2 gnd Vektorverband (DE-588)4187471-7 gnd Funktionenraum (DE-588)4134834-5 gnd |
| topic_facet | MATHEMATICS / Transformations Function spaces Narrow operators Riesz spaces Operator Vektorverband Funktionenraum |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=530546 |
| work_keys_str_mv | AT popovmykhailomykhailovych narrowoperatorsonfunctionspacesandvectorlattices AT randrianantoaninabeata narrowoperatorsonfunctionspacesandvectorlattices |