Banach Spaces for Analysts

P. Wojtaszczyk

doi:10.1017/CBO9780511608735

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P. Wojtaszczyk, Uniwersytet Warszawski, Poland

Publisher:: Cambridge University Press
Online publication date:: May 2010
Print publication year:: 1991
Online ISBN:: 9780511608735
DOI:: https://doi.org/10.1017/CBO9780511608735

Subjects:: Mathematics (general), Mathematics, Abstract Analysis
Series:: Cambridge Studies in Advanced Mathematics (25)

49.99 (GBP)

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This is an introduction to modern Banach space theory, in which applications to other areas such as harmonic analysis function theory, orthogonal series and approximation theory are also given prominence. The author begins with a discussion of weak topologies, weak compactness and isomorphisms of Banach spaces before proceeding to the more detailed study of particular spaces. The book is intended to be used with graduate courses in Banach space theory, so the prerequisites are a background in functional, complex and real analysis. As the only introduction to the modern theory it will be an essential companion for professional mathematicians working in the subject, or interested in applying it to other areas of analysis.

‘… a detailed and self-contained discussion.’

Source: L’Enseignement Mathématique

‘… a very welcome addition to the literature on Banach spaces.’

Source: Bulletin of the LMS

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Banach Spaces for Analysts

This Book has been cited by the following publications. This list is generated based on data provided by Crossref.

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Contents

Frontmatter
pp i-iv

Contents
pp v-viii

Preface
pp ix-xiv

Part I - Introduction
pp 1-2

I.A - Functional analysis
pp 3-8

I.B - Examples of spaces and operators
pp 9-26

Part II - Basic concepts of Banach space theory

II.A - Weak topologies
pp 27-34

II.B - Isomorphisms, bases, projections
pp 35-48

II.C - Weak compactness
pp 49-56

II.D - Convergence of series
pp 57-68

II.E - Local properties
pp 69-82

Part III - Selected topics

III.A - Lp-spaces; type and cotype
pp 83-110

III.B - Projection constants
pp 111-130

III.C - L1(μ)-spaces
pp 131-150

III.D - C(K)-spaces
pp 151-180

III.E - The disc algebra
pp 181-198

III.F - Absolutely summing and related operators
pp 199-236

III.G - Schatten-von Neumann classes
pp 237-256

III.H - Factorization theorems
pp 257-290

III.I - Absolutely summing operators on the disc algebra
pp 291-322

Hints for the exercises
pp 323-340

List of symbols
pp 341-344

References
pp 345-376

Index
pp 377-382

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Banach Spaces for Analysts

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Contents

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