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Narrow operators on function spaces and vector lattices

Author: Mykhaĭlo Mykhaĭlovych Popov; Beata Randrianantoanina
Publisher: Berlin : De Gruyter, [2013]
Series: De Gruyter studies in mathematics, 45.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
"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  Read more...
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Document Type: Book
All Authors / Contributors: Mykhaĭlo Mykhaĭlovych Popov; Beata Randrianantoanina
ISBN: 9783110263039 3110263033 9783119163798 3119163791
OCLC Number: 818735918
Description: xiii, 319 pages ; 25 cm.
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.
Series Title: De Gruyter studies in mathematics, 45.
Responsibility: by Mikhail Popov, Beata Randrianantoanina.

Abstract:

Narrow operators are those operators defined on function spaces which are "small'' at signs, i.e. Numerous works and research papers exist on these, but no coherent monograph yet to place them in  Read more...
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"[...] This monograph presents many interesting and deep results revolving around the notion of a narrow operator. The theorems are well motivated and the proofs are very detailed. The authors have Read more...

 
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