Lecture Notes in Mathematics
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Banach Spaces and Descriptive Set Theory: Selected Topics

Authors: Dodos, Pandelis

  • The author has been a central player in new developments of this area
  • This book is a much needed exposition
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  • ISBN 978-3-642-12153-1
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About this book

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.

Reviews

From the reviews:

“The book under review … is mainly focused on the author’s work on characterizations of the existence of universal elements in subclasses of separable Banach spaces … . The book collects the most important of these results into a self-contained framework that clarifies the ideas under the successive improvements between each paper and the following ones. All this makes the book a mandatory reference for anyone interested in universality in Banach spaces.” (Matias Raja, Mathematical Reviews, Issue 2011 j)

“The author uses descriptive set theory to prove results on the structure of Banach spaces. … this book may be useful for people interested in Banach space theory or/and descriptive set theory. It is very well written and contains a lot of results and techniques from these two theories, and thus may serve as a reference book.” (Daniel Li, Zentralblatt MATH, Vol. 1215, 2011)


Table of contents (7 chapters)

Table of contents (7 chapters)
  • Basic Concepts

    Dodos, Pandelis

    Pages 1-8

  • The Standard Borel Space of All Separable Banach Spaces

    Dodos, Pandelis

    Pages 9-35

  • The ℓ2 Baire Sum

    Dodos, Pandelis

    Pages 37-56

  • Amalgamated Spaces

    Dodos, Pandelis

    Pages 57-70

  • Zippin’s Embedding Theorem

    Dodos, Pandelis

    Pages 71-88

Buy this book

eBook $34.99
price for USA in USD (gross)
  • ISBN 978-3-642-12153-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.95
price for USA in USD
  • ISBN 978-3-642-12152-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Banach Spaces and Descriptive Set Theory: Selected Topics
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1993
Copyright
2010
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-12153-1
DOI
10.1007/978-3-642-12153-1
Softcover ISBN
978-3-642-12152-4
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XII, 168
Topics