عنوان

Narrow operators on function spaces and vector lattices /

Terms of Availability and/or Price

(hardcover : alk. paper)

Terms of Availability and/or Price

(hardcover + e-book))

Terms of Availability and/or Price

(hardcover : alk. paper)

Terms of Availability and/or Price

(hardcover + e-book))

Terms of Availability and/or Price

(e-book)

(Number (ISBN

3110263033

(Number (ISBN

3119163791 (set

(Number (ISBN

9783110263039

(Number (ISBN

9783119163798 (set

Erroneous ISBN

9783110263343

Number

dltt

Title Proper

Narrow operators on function spaces and vector lattices /

General Material Designation

[Book]

First Statement of Responsibility

by Mikhail Popov, Beata Randrianantoanina

Specific Material Designation and Extent of Item

xiii, 319 pages ;

Dimensions

25 cm

Series Title

De Gruyter studies in mathematics ;

Volume Designation

45

Text of Note

Includes bibliographical references (pages 307-314) and indexes

Text of Note

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

0

Text of Note

"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

Function spaces

Narrow operators

Riesz spaces

Class number

Book number

Popov, Mykhaĭlo Mykhaĭlovych

Randrianantoanina, Beata

Date of Transaction

20150610002018.0

Cataloguing Rules (Descriptive Conventions))

rda

Electronic name

[Book]

Y