Narrow Operators on Function Spaces and Vector Lattices / / Mikhail Popov, Beata Randrianantoanina.
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 conside...
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Popov, Mikhail, author. aut http://id.loc.gov/vocabulary/relators/aut Narrow Operators on Function Spaces and Vector Lattices / Mikhail Popov, Beata Randrianantoanina. Berlin ; Boston : De Gruyter, [2012] ©2012 1 online resource (319 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda De Gruyter Studies in Mathematics , 0179-0986 ; 45 Frontmatter -- Preface -- Contents -- Chapter 1. Introduction and preliminaries -- Chapter 2. Each “small” operator is narrow -- Chapter 3. Some properties of narrow operators with applications to nonlocally convex spaces -- Chapter 4. Noncompact narrow operators -- Chapter 5. Ideal properties, conjugates, spectrum and numerical radii of narrow operators -- Chapter 6. Daugavet-type properties of Lebesgue and Lorentz spaces -- Chapter 7. Strict singularity versus narrowness -- Chapter 8. Weak embeddings of L1 -- Chapter 9. Spaces X for which every operator T ∈ ℒ (Lp;X) is narrow -- Chapter 10. Narrow operators on vector lattices -- Chapter 11. Some variants of the notion of narrow operators -- Chapter 12. Open problems -- Bibliography -- Index of names -- Subject index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star 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. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 28. Feb 2023) Function spaces. Narrow operators. Riesz spaces. MATHEMATICS / Mathematical Analysis. bisacsh Function Space. Narrow Operator. Vector Lattice. Randrianantoanina, Beata, author. aut http://id.loc.gov/vocabulary/relators/aut Title is part of eBook package: De Gruyter DG Studies in Mathematics eBook-Package 9783110494938 ZDB-23-GSM Title is part of eBook package: De Gruyter DGBA Backlist Complete English Language 2000-2014 PART1 9783110238570 Title is part of eBook package: De Gruyter DGBA Backlist Mathematics 2000-2014 (EN) 9783110238471 Title is part of eBook package: De Gruyter DGBA Mathematics - 2000 - 2014 9783110637205 ZDB-23-GMA Title is part of eBook package: De Gruyter E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2012 9783110288995 ZDB-23-DGG Title is part of eBook package: De Gruyter E-BOOK PACKAGE MATHEMATICS, PHYSICS, ENGINEERING 2012 9783110293722 ZDB-23-DMI Title is part of eBook package: De Gruyter E-BOOK PAKET MATHEMATIK, PHYSIK, INGENIEURWISS. 2012 9783110288926 ZDB-23-DMP print 9783110263039 https://doi.org/10.1515/9783110263343 https://www.degruyter.com/isbn/9783110263343 Cover https://www.degruyter.com/document/cover/isbn/9783110263343/original |
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English |
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eBook |
author |
Popov, Mikhail, Popov, Mikhail, Randrianantoanina, Beata, |
spellingShingle |
Popov, Mikhail, Popov, Mikhail, Randrianantoanina, Beata, Narrow Operators on Function Spaces and Vector Lattices / De Gruyter Studies in Mathematics , Frontmatter -- Preface -- Contents -- Chapter 1. Introduction and preliminaries -- Chapter 2. Each “small” operator is narrow -- Chapter 3. Some properties of narrow operators with applications to nonlocally convex spaces -- Chapter 4. Noncompact narrow operators -- Chapter 5. Ideal properties, conjugates, spectrum and numerical radii of narrow operators -- Chapter 6. Daugavet-type properties of Lebesgue and Lorentz spaces -- Chapter 7. Strict singularity versus narrowness -- Chapter 8. Weak embeddings of L1 -- Chapter 9. Spaces X for which every operator T ∈ ℒ (Lp;X) is narrow -- Chapter 10. Narrow operators on vector lattices -- Chapter 11. Some variants of the notion of narrow operators -- Chapter 12. Open problems -- Bibliography -- Index of names -- Subject index |
author_facet |
Popov, Mikhail, Popov, Mikhail, Randrianantoanina, Beata, Randrianantoanina, Beata, Randrianantoanina, Beata, |
author_variant |
m p mp m p mp b r br |
author_role |
VerfasserIn VerfasserIn VerfasserIn |
author2 |
Randrianantoanina, Beata, Randrianantoanina, Beata, |
author2_variant |
b r br |
author2_role |
VerfasserIn VerfasserIn |
author_sort |
Popov, Mikhail, |
title |
Narrow Operators on Function Spaces and Vector Lattices / |
title_full |
Narrow Operators on Function Spaces and Vector Lattices / Mikhail Popov, Beata Randrianantoanina. |
title_fullStr |
Narrow Operators on Function Spaces and Vector Lattices / Mikhail Popov, Beata Randrianantoanina. |
title_full_unstemmed |
Narrow Operators on Function Spaces and Vector Lattices / Mikhail Popov, Beata Randrianantoanina. |
title_auth |
Narrow Operators on Function Spaces and Vector Lattices / |
title_alt |
Frontmatter -- Preface -- Contents -- Chapter 1. Introduction and preliminaries -- Chapter 2. Each “small” operator is narrow -- Chapter 3. Some properties of narrow operators with applications to nonlocally convex spaces -- Chapter 4. Noncompact narrow operators -- Chapter 5. Ideal properties, conjugates, spectrum and numerical radii of narrow operators -- Chapter 6. Daugavet-type properties of Lebesgue and Lorentz spaces -- Chapter 7. Strict singularity versus narrowness -- Chapter 8. Weak embeddings of L1 -- Chapter 9. Spaces X for which every operator T ∈ ℒ (Lp;X) is narrow -- Chapter 10. Narrow operators on vector lattices -- Chapter 11. Some variants of the notion of narrow operators -- Chapter 12. Open problems -- Bibliography -- Index of names -- Subject index |
title_new |
Narrow Operators on Function Spaces and Vector Lattices / |
title_sort |
narrow operators on function spaces and vector lattices / |
series |
De Gruyter Studies in Mathematics , |
series2 |
De Gruyter Studies in Mathematics , |
publisher |
De Gruyter, |
publishDate |
2012 |
physical |
1 online resource (319 p.) Issued also in print. |
contents |
Frontmatter -- Preface -- Contents -- Chapter 1. Introduction and preliminaries -- Chapter 2. Each “small” operator is narrow -- Chapter 3. Some properties of narrow operators with applications to nonlocally convex spaces -- Chapter 4. Noncompact narrow operators -- Chapter 5. Ideal properties, conjugates, spectrum and numerical radii of narrow operators -- Chapter 6. Daugavet-type properties of Lebesgue and Lorentz spaces -- Chapter 7. Strict singularity versus narrowness -- Chapter 8. Weak embeddings of L1 -- Chapter 9. Spaces X for which every operator T ∈ ℒ (Lp;X) is narrow -- Chapter 10. Narrow operators on vector lattices -- Chapter 11. Some variants of the notion of narrow operators -- Chapter 12. Open problems -- Bibliography -- Index of names -- Subject index |
isbn |
9783110263343 9783110494938 9783110238570 9783110238471 9783110637205 9783110288995 9783110293722 9783110288926 9783110263039 |
issn |
0179-0986 ; |
url |
https://doi.org/10.1515/9783110263343 https://www.degruyter.com/isbn/9783110263343 https://www.degruyter.com/document/cover/isbn/9783110263343/original |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
515 - Analysis |
dewey-full |
515.73 |
dewey-sort |
3515.73 |
dewey-raw |
515.73 |
dewey-search |
515.73 |
doi_str_mv |
10.1515/9783110263343 |
oclc_num |
853248751 |
work_keys_str_mv |
AT popovmikhail narrowoperatorsonfunctionspacesandvectorlattices AT randrianantoaninabeata narrowoperatorsonfunctionspacesandvectorlattices |
status_str |
n |
ids_txt_mv |
(DE-B1597)172141 (OCoLC)853248751 |
carrierType_str_mv |
cr |
hierarchy_parent_title |
Title is part of eBook package: De Gruyter DG Studies in Mathematics eBook-Package Title is part of eBook package: De Gruyter DGBA Backlist Complete English Language 2000-2014 PART1 Title is part of eBook package: De Gruyter DGBA Backlist Mathematics 2000-2014 (EN) Title is part of eBook package: De Gruyter DGBA Mathematics - 2000 - 2014 Title is part of eBook package: De Gruyter E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2012 Title is part of eBook package: De Gruyter E-BOOK PACKAGE MATHEMATICS, PHYSICS, ENGINEERING 2012 Title is part of eBook package: De Gruyter E-BOOK PAKET MATHEMATIK, PHYSIK, INGENIEURWISS. 2012 |
is_hierarchy_title |
Narrow Operators on Function Spaces and Vector Lattices / |
container_title |
Title is part of eBook package: De Gruyter DG Studies in Mathematics eBook-Package |
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