Narrow operators on function spaces and vector lattices
By: by Mikhail Popov, Beata Randrianantoanina
Contributors: Randrianantoanina, Beata; Walter de Gruyter & Co
Series: De Gruyter studies in mathematics -- 45
Publisher: De Gruyter
Published: 2013
Language: eng
Format: [electronic resource] /
Number of pages: 319
ISBN-13: 9783110263039; 9783110263343; 9783119163798
Subjects: Riesz spaces; Function spaces; Narrow operators
Description: "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.
Notes: Includes bibliographical references and indexes.