Banach spaces for analysts

✍ Scribed by Przemysław Wojtaszczyk

• Publisher: Cambridge University Press
• Year: 1991
• Tongue: English
• Leaves: 397
• Category: Library

✦ Synopsis

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 of Banach spaces, it will be an essential companion for professional mathematicians working in the subject, or to those interested in applying it to other areas of analysis.

✦ Table of Contents

Front Cover......Page 1
Title......Page 3
Contents......Page 5
Preface......Page 9
PART I. INTRODUCTION......Page 15
I.A. Functional analysis......Page 17
I.B. Examples of spaces and operators......Page 23
II.A. Weak topologies......Page 41
II.B. Isomorphisms, bases, projections......Page 49
II.C. Weak compactness......Page 63
II.D. Convergence of series......Page 71
II.E. Local properties......Page 83
III.A. Lp-spaces; type and cotype......Page 97
III.B. Projection constants......Page 125
III.C. L1(μ)-spaces......Page 145
III.D. C(K)-spaces......Page 165
III.E. The disc algebra......Page 195
III.F. Absolutely summing and related operators......Page 213
III.G. Schatten-von Neumann classes......Page 251
III.H. Factorization theorems......Page 271
III.I. Absolutely summing operators on the disc algebra......Page 305
II.B......Page 337
II.C......Page 338
II.D......Page 339
II.E......Page 340
III.A......Page 341
III.B......Page 342
III.C......Page 343
III.D......Page 344
III.E......Page 347
III.F......Page 348
III.G......Page 349
III.H......Page 350
III.I......Page 351
List of symbols......Page 355
References......Page 359
Index......Page 391
Back Cover......Page 397