M-Ideals in Banach Spaces and Banach Algebras

1. Front Matter

   Pages I-VIII

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2. Basic theory of M-ideals

   • Peter Harmand, Dirk Werner, Wend Werner

   Pages 1-47

3. Geometric properties of M-ideals

   • Peter Harmand, Dirk Werner, Wend Werner

   Pages 49-100

4. Banach spaces which are M-ideals in their biduals

   • Peter Harmand, Dirk Werner, Wend Werner

   Pages 101-155

5. Banach spaces which are L-summands in their biduals

   • Peter Harmand, Dirk Werner, Wend Werner

   Pages 157-214

6. M-ideals in Banach algebras

   • Peter Harmand, Dirk Werner, Wend Werner

   Pages 215-261

7. M-ideals in spaces of bounded operators

   • Peter Harmand, Dirk Werner, Wend Werner

   Pages 263-344

8. Back Matter

   Pages 345-387

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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.

• Banach Algebras
• Banach Space
• C*-algebra
• Operators
• functional analysis

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