دانلود کتاب Rearrangements of Series in Banach Spaces

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Cover Rearrangements of Series in Banach Spaces Copyright ©1991 by the American Mathematical Society ISBN 0-8218-4546-2 QA295.K2813 1991 512'.55-dc20 LCCN 91-6522 CIP Contents Introduction CHAPTER 1 General Information §1.1. Numerical series. The Riemann theorem §1.2. Basic definitions. Elementary properties of vector series § 1.3. Preliminary information about rearrangements of series of elements of a Banach space CHAPTER 2 Conditionally Convergent Series §2.1. The domain of sums of a series in a finite-dimensional normed space §2.2. Conditional convergence in an infinite-dimensional space. General results §2.3. Conditionally convergent series in the spaces Lp CHAPTER 3 Unconditionally Convergent Series §3.1. The Dvoretzky-Rogers theorem §3.2. The Orlicz theorem on unconditionally convergent series in the spaces Lp §3.3. Absolutely summing operators CHAPTER 4 Some Results in the General Theoryof Banach Spaces §4.1. Finite representability §4.2. Frechet differentiability of convex functions §4.3. The Dvoretzky theorem §4.4. Basic sequences §4.5. Some applications to conditionally convergent series CHAPTER 5 M-cotype and the Orlicz Theorem §5.1. Unconditionally convergent series in the space Co §5.2. C-convexity and the Orlicz theorem §5.3. Summary of results on type and cotype CHAPTER 6 The Steinitz Theorem and B-Convexity §6.1. Conditionally convergent series in spaces with an infratype §6.2. Series in spaces that are not B-convex §6.3. The Chobanyan inequality §6.4. Survey of unsolved problems in the theory of series Comments on the Exercises Chapter 1 Chapter 2 Chapter 3, Chapter 4 Chapter 5 Chapter 6 Bibliography Subject Index Back Cover