UID:
almahu_9949462112802882
Format:
1 online resource (319 p.)
ISBN:
9783110263343
,
9783110494938
Series Statement:
De Gruyter Studies in Mathematics , 45
Content:
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.
Note:
Frontmatter --
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Preface --
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Contents --
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Chapter 1. Introduction and preliminaries --
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Chapter 2. Each "small" operator is narrow --
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Chapter 3. Some properties of narrow operators with applications to nonlocally convex spaces --
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Chapter 4. Noncompact narrow operators --
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Chapter 5. Ideal properties, conjugates, spectrum and numerical radii of narrow operators --
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Chapter 6. Daugavet-type properties of Lebesgue and Lorentz spaces --
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Chapter 7. Strict singularity versus narrowness --
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Chapter 8. Weak embeddings of L1 --
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Chapter 9. Spaces X for which every operator T ∈ ℒ (Lp;X) is narrow --
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Chapter 10. Narrow operators on vector lattices --
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Chapter 11. Some variants of the notion of narrow operators --
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Chapter 12. Open problems --
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Bibliography --
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Index of names --
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Subject index
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Issued also in print.
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Mode of access: Internet via World Wide Web.
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In English.
In:
DG Studies in Mathematics eBook-Package, De Gruyter, 9783110494938
In:
DGBA Backlist Complete English Language 2000-2014 PART1, De Gruyter, 9783110238570
In:
DGBA Backlist Mathematics 2000-2014 (EN), De Gruyter, 9783110238471
In:
DGBA Mathematics - 2000 - 2014, De Gruyter, 9783110637205
In:
E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2012, De Gruyter, 9783110288995
In:
E-BOOK PACKAGE MATHEMATICS, PHYSICS, ENGINEERING 2012, De Gruyter, 9783110293722
In:
E-BOOK PAKET MATHEMATIK, PHYSIK, INGENIEURWISS. 2012, De Gruyter, 9783110288926
Additional Edition:
ISBN 9783110263039
Language:
English
Subjects:
Mathematics
DOI:
10.1515/9783110263343
URL:
https://doi.org/10.1515/9783110263343
URL:
https://www.degruyter.com/isbn/9783110263343
