Skip to main content
SpringerLink
Log in
Birkhäuser

Köthe-Bochner Function Spaces

  • Book
  • © 2004

Overview

Authors:
  1. Pei-Kee Lin

    1. Department of Mathematics, University of Memphis, Memphis, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Contains recent results of the geometric properties in the K(oe)the-Bochner spaces
  • Each section is independent of each other, allowing the different levels of readership

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (6 chapters)

  1. Front Matter

    Pages i-xiii
    Download chapter PDF

  2. Classical Theorems

    • Pei-Kee Lin
    Pages 1-100

  3. Convexity and Smoothness

    • Pei-Kee Lin
    Pages 101-142

  4. Köthe-Bochner Function Spaces

    • Pei-Kee Lin
    Pages 143-218

  5. Stability Properties I

    • Pei-Kee Lin
    Pages 219-246

  6. Stability Properties II

    • Pei-Kee Lin
    Pages 247-312

  7. Continuous Function Spaces

    • Pei-Kee Lin
    Pages 313-366

  8. Back Matter

    Pages 367-370
    Download chapter PDF
Back to top

Keywords

About this book

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.

Reviews

From the reviews:

"This book is a nice and useful reference for researchers in functional analysis who wish to have a quite comprehensive survey of geometric properties of Banach spaces of vector-valued functions." ---Mathematical Reviews

“This book … gives in fact an exhaustive and very up-to-date account of several aspects of the general theory (isomorphic) and geometry of Banach spaces. This book is self-contained with an exhaustive list of references at the end of each chapter. Apart from well thought-out exercises at the end of each section, the `Notes and Remarks’ section at the end of each chapter contains several open questions with additional comments and references. This book is worth having on the shelves of anyone interested in Banach space theory. I thoroughly enjoyed going through it.”(ZENTRALBLATT MATH)

"This book, though somewahte restrictively entitled, gives in fact an exhaustive and very up-to-date account of several aspects of the general theory (isomorphic) and geometry of Banach spaces. . . This book is self-contained with an exhaustive list of references at the end of each chapter. Apart from well thoght-out exervises at the end of each section,t he 'Notes and Remarks' section at the end of each chapter contains several open questions with additional somments and references. This book is worth having on the shelves of anyone interested in Banach space theory.  I thoroughly enjoyed going through it."

---Zenteralblatt MATH

 

Authors and Affiliations

  • Department of Mathematics, University of Memphis, Memphis, USA

    Pei-Kee Lin

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation