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Tsirelson's Space

  • Book
  • © 1989

Overview

Authors:
  1. Peter G. Casazza
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  2. Thaddeus J. Shura
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1363)

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About this book

This monograph provides a structure theory for the increasingly important Banach space discovered by B.S. Tsirelson. The basic construction should be accessible to graduate students of functional analysis with a knowledge of the theory of Schauder bases, while topics of a more advanced nature are presented for the specialist. Bounded linear operators are studied through the use of finite-dimensional decompositions, and complemented subspaces are studied at length. A myriad of variant constructions are presented and explored, while open questions are broached in almost every chapter. Two appendices are attached: one dealing with a computer program which computes norms of finitely-supported vectors, while the other surveys recent work on weak Hilbert spaces (where a Tsirelson-type space provides an example).

Keywords

Table of contents (12 chapters)

  1. Front Matter

    Pages I-VIII
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  2. Precursors of the Tsirelson construction

    • Peter G. Casazza, Thaddeus J. Shura
    Pages 1-7

  3. The Figiel-Johnson construction of Tsirelson's space

    • Peter G. Casazza, Thaddeus J. Shura
    Pages 8-18

  4. Block basic sequences in Tsirelson's space

    • Peter G. Casazza, Thaddeus J. Shura
    Pages 19-23

  5. Bounded linear operators on T and the “blocking” principle

    • Peter G. Casazza, Thaddeus J. Shura
    Pages 24-34

  6. Subsequences of the unit vector basis of Tsirelson's space

    • Peter G. Casazza, Thaddeus J. Shura
    Pages 35-47

  7. Modified Tsirelson's Space: TM

    • Peter G. Casazza, Thaddeus J. Shura
    Pages 48-53

  8. Embedding Theorems about T and T

    • Peter G. Casazza, Thaddeus J. Shura
    Pages 54-59

  9. Isomorphisms between subspaces of Tsirelson's space which are spanned by subsequences of \(\left\{ {t_n } \right\}_{n = 1}^\infty\)

    • Peter G. Casazza, Thaddeus J. Shura
    Pages 60-66

  10. Permutations of the unit vector basis of Tsirelson's space

    • Peter G. Casazza, Thaddeus J. Shura
    Pages 67-81

  11. Unconditional bases for complemented subspaces of Tsirelson's space

    • Peter G. Casazza, Thaddeus J. Shura
    Pages 82-94

  12. Variations on a Theme

    • Peter G. Casazza, Thaddeus J. Shura
    Pages 95-118

  13. Some final comments

    • Peter G. Casazza, Thaddeus J. Shura
    Pages 119-120

  14. Back Matter

    Pages 121-204
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Bibliographic Information

  • Book Title: Tsirelson's Space

  • Authors: Peter G. Casazza, Thaddeus J. Shura

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0085267

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1989

  • Softcover ISBN: 978-3-540-50678-2Published: 11 January 1989

  • eBook ISBN: 978-3-540-46069-5Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: X, 206

  • Topics: Analysis

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