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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Superior document: | Title is part of eBook package: De Gruyter DG Studies in Mathematics eBook-Package |
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Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2012] ©2012 |
Year of Publication: | 2012 |
Language: | English |
Series: | De Gruyter Studies in Mathematics ,
45 |
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Physical Description: | 1 online resource (319 p.) |
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100 | 1 | |a Popov, Mikhail, |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
245 | 1 | 0 | |a Narrow Operators on Function Spaces and Vector Lattices / |c Mikhail Popov, Beata Randrianantoanina. |
264 | 1 | |a Berlin ; |a Boston : |b De Gruyter, |c [2012] | |
264 | 4 | |c ©2012 | |
300 | |a 1 online resource (319 p.) | ||
336 | |a text |b txt |2 rdacontent | ||
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347 | |a text file |b PDF |2 rda | ||
490 | 0 | |a De Gruyter Studies in Mathematics , |x 0179-0986 ; |v 45 | |
505 | 0 | 0 | |t Frontmatter -- |t Preface -- |t Contents -- |t Chapter 1. Introduction and preliminaries -- |t Chapter 2. Each “small” operator is narrow -- |t Chapter 3. Some properties of narrow operators with applications to nonlocally convex spaces -- |t Chapter 4. Noncompact narrow operators -- |t Chapter 5. Ideal properties, conjugates, spectrum and numerical radii of narrow operators -- |t Chapter 6. Daugavet-type properties of Lebesgue and Lorentz spaces -- |t Chapter 7. Strict singularity versus narrowness -- |t Chapter 8. Weak embeddings of L1 -- |t Chapter 9. Spaces X for which every operator T ∈ ℒ (Lp;X) is narrow -- |t Chapter 10. Narrow operators on vector lattices -- |t Chapter 11. Some variants of the notion of narrow operators -- |t Chapter 12. Open problems -- |t Bibliography -- |t Index of names -- |t Subject index |
506 | 0 | |a restricted access |u http://purl.org/coar/access_right/c_16ec |f online access with authorization |2 star | |
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. | ||
530 | |a Issued also in print. | ||
538 | |a Mode of access: Internet via World Wide Web. | ||
546 | |a In English. | ||
588 | 0 | |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 28. Feb 2023) | |
650 | 0 | |a Function spaces. | |
650 | 0 | |a Narrow operators. | |
650 | 0 | |a Riesz spaces. | |
650 | 7 | |a MATHEMATICS / Mathematical Analysis. |2 bisacsh | |
653 | |a Function Space. | ||
653 | |a Narrow Operator. | ||
653 | |a Vector Lattice. | ||
700 | 1 | |a Randrianantoanina, Beata, |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t DG Studies in Mathematics eBook-Package |z 9783110494938 |o ZDB-23-GSM |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t DGBA Backlist Complete English Language 2000-2014 PART1 |z 9783110238570 |
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773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t DGBA Mathematics - 2000 - 2014 |z 9783110637205 |o ZDB-23-GMA |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2012 |z 9783110288995 |o ZDB-23-DGG |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t E-BOOK PACKAGE MATHEMATICS, PHYSICS, ENGINEERING 2012 |z 9783110293722 |o ZDB-23-DMI |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t E-BOOK PAKET MATHEMATIK, PHYSIK, INGENIEURWISS. 2012 |z 9783110288926 |o ZDB-23-DMP |
776 | 0 | |c print |z 9783110263039 | |
856 | 4 | 0 | |u https://doi.org/10.1515/9783110263343 |
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