Banach Spaces and Descriptive Set Theory: Selected Topics

  • Pandelis Dodos

Part of the Lecture Notes in Mathematics book series (LNM, volume 1993)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Pandelis Dodos
    Pages 1-8
  3. Pandelis Dodos
    Pages 37-56
  4. Pandelis Dodos
    Pages 57-70
  5. Pandelis Dodos
    Pages 71-88
  6. Pandelis Dodos
    Pages 89-114
  7. Pandelis Dodos
    Pages 115-126
  8. Back Matter
    Pages 127-167

About this book

Introduction

This volume deals with problems in the structure theory of separable infinite-dimensional Banach spaces, with a central focus on universality problems. This topic goes back to the beginnings of the field and appears in Banach's classical monograph. The novelty of the approach lies in the fact that the answers to a number of basic questions are based on techniques from Descriptive Set Theory. Although the book is oriented on proofs of several structural theorems, in the main text readers will also find a detailed exposition of numerous “intermediate” results which are interesting in their own right and have proven to be useful in other areas of Functional Analysis. Moreover, several well-known results in the geometry of Banach spaces are presented from a modern perspective.

Keywords

Finite Graph calculus function functional analysis geometry proof set theory theorem

Authors and affiliations

  • Pandelis Dodos
    • 1
  1. 1.University of AthensAthensGreece

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-12153-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 2010
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-12152-4
  • Online ISBN 978-3-642-12153-1
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book