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Advanced Courses in Mathematics - CRM Barcelona
cover

Ramsey Methods in Analysis

Authors: Argyros, Spiros A., Todorcevic, Stevo

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eBook 32,99 €
price for Spain (gross)
  • ISBN 978-3-7643-7360-3
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  • Immediate eBook download after purchase
Softcover 41,50 €
price for Spain (gross)
  • ISBN 978-3-7643-7264-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this Textbook

This book introduces graduate students and resarchers to the study of the geometry of Banach spaces using combinatorial methods. The combinatorial, and in particular the Ramsey-theoretic, approach to Banach space theory is not new, it can be traced back as early as the 1970s. Its full appreciation, however, came only during the last decade or so, after some of the most important problems in Banach space theory were solved, such as, for example, the distortion problem, the unconditional basic sequence problem, and the homogeneous space problem. The book covers most of these advances, but one of its primary purposes is to discuss some of the recent advances that are not present in survey articles of these areas. We show, for example, how to introduce a conditional structure to a given Banach space under construction that allows us to essentially prescribe the corresponding space of non-strictly singular operators. We also apply the Nash-Williams theory of fronts and barriers in the study of Cezaro summability and unconditionality present in basic sequences inside a given Banach space. We further provide a detailed exposition of the block-Ramsey theory and its recent deep adjustments relevant to the Banach space theory due to Gowers.

Reviews

"This book is the result of lectures given by the authors aimed at bringing young researchers to the forefront of a ‘very active research area lying on the borderline between analysis and combinatorics’…This book will certainly be appreciated by experts. It is also valuable for young researchers who are suitably prepared and wish to work in this amazing area."   —Mathematical Reviews

"The book is carefully written with clear exposition of the material. It can be studied by graduate students who had a first course in functional analysis and are interested in either functional analysis or Ramsey theory."   —Zentralblatt MATH


Table of contents (18 chapters)

Table of contents (18 chapters)
  • Introduction

    Pages 3-6

  • Tsirelson and Mixed Tsirelson Spaces

    Pages 7-19

  • Tree Complete Extensions of a Ground Norm

    Pages 21-38

  • Hereditarily Indecomposable Extensions with a Schauder Basis

    Pages 39-46

  • The Space of the Operators for Hereditarily Indecomposable Banach Spaces

    Pages 47-55

Buy this book

eBook 32,99 €
price for Spain (gross)
  • ISBN 978-3-7643-7360-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 41,50 €
price for Spain (gross)
  • ISBN 978-3-7643-7264-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Ramsey Methods in Analysis
Authors
Series Title
Advanced Courses in Mathematics - CRM Barcelona
Copyright
2005
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Basel
eBook ISBN
978-3-7643-7360-3
DOI
10.1007/3-7643-7360-1
Softcover ISBN
978-3-7643-7264-4
Series ISSN
2297-0304
Edition Number
1
Number of Pages
VI, 257
Topics