M-Ideals in Banach Spaces and Banach Algebras
Harmand, Peter.
M-Ideals in Banach Spaces and Banach Algebras [electronic resource] / by Peter Harmand, Dirk Werner, Wend Werner. - VIII, 396 p. online resource. - Lecture Notes in Mathematics, 1547 0075-8434 ; . - Lecture Notes in Mathematics, 1547 .
Basic theory of M-ideals -- Geometric properties of M-ideals -- Banach spaces which are M-ideals in their biduals -- Banach spaces which are L-summands in their biduals -- M-ideals in Banach algebras -- M-ideals in spaces of bounded operators.
This book provides a comprehensive exposition of M-ideal theory, a branch ofgeometric functional analysis which deals with certain subspaces of Banach spaces arising naturally in many contexts. Starting from the basic definitions the authors discuss a number of examples of M-ideals (e.g. the closed two-sided ideals of C*-algebras) and develop their general theory. Besides, applications to problems from a variety of areas including approximation theory, harmonic analysis, C*-algebra theory and Banach space geometry are presented. The book is mainly intended as a reference volume for researchers working in one of these fields, but it also addresses students at the graduate or postgraduate level. Each of its six chapters is accompanied by a Notes-and-Remarks section which explores further ramifications of the subject and gives detailed references to the literature. An extensive bibliography is included.
9783540477532
10.1007/BFb0084355 doi
Global analysis (Mathematics).
Analysis.
QA299.6-433
515
M-Ideals in Banach Spaces and Banach Algebras [electronic resource] / by Peter Harmand, Dirk Werner, Wend Werner. - VIII, 396 p. online resource. - Lecture Notes in Mathematics, 1547 0075-8434 ; . - Lecture Notes in Mathematics, 1547 .
Basic theory of M-ideals -- Geometric properties of M-ideals -- Banach spaces which are M-ideals in their biduals -- Banach spaces which are L-summands in their biduals -- M-ideals in Banach algebras -- M-ideals in spaces of bounded operators.
This book provides a comprehensive exposition of M-ideal theory, a branch ofgeometric functional analysis which deals with certain subspaces of Banach spaces arising naturally in many contexts. Starting from the basic definitions the authors discuss a number of examples of M-ideals (e.g. the closed two-sided ideals of C*-algebras) and develop their general theory. Besides, applications to problems from a variety of areas including approximation theory, harmonic analysis, C*-algebra theory and Banach space geometry are presented. The book is mainly intended as a reference volume for researchers working in one of these fields, but it also addresses students at the graduate or postgraduate level. Each of its six chapters is accompanied by a Notes-and-Remarks section which explores further ramifications of the subject and gives detailed references to the literature. An extensive bibliography is included.
9783540477532
10.1007/BFb0084355 doi
Global analysis (Mathematics).
Analysis.
QA299.6-433
515