Pandelis Dodos

Banach Spaces and Descriptive Set Theory: Selected Topics (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer-Verlag GmbH
• Seitenzahl: 168
• Erscheinungstermin: 15. April 2010
• Englisch
• ISBN-13: 9783642121531
• Artikelnr.: 44227521

Inhaltsangabe

Basic Concepts.- The Standard Borel Space of All Separable Banach Spaces.- The ?2 Baire Sum.- Amalgamated Spaces.- Zippin's Embedding Theorem.- The Bourgain-Pisier Construction.- Strongly Bounded Classes of Banach Spaces.

Rezensionen

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)