Ramsey Methods in Analysis

Authors:

ISBN: 978-3-7643-7264-4 (Print) 978-3-7643-7360-3 (Online)

Table of contents (18 chapters)

  1. Saturated and Conditional Structures in Banach Spaces

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      Book Chapter

      Pages 3-6

      Introduction

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      Book Chapter

      Pages 7-19

      Tsirelson and Mixed Tsirelson Spaces

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      Book Chapter

      Pages 21-38

      Tree Complete Extensions of a Ground Norm

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      Book Chapter

      Pages 39-46

      Hereditarily Indecomposable Extensions with a Schauder Basis

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      Book Chapter

      Pages 47-55

      The Space of the Operators for Hereditarily Indecomposable Banach Spaces

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      Book Chapter

      Pages 57-70

      Examples of Hereditarily Indecomposable Extensions

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      Book Chapter

      Pages 71-79

      The Space \(\mathfrak{X}\omega _1 \)

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      Book Chapter

      Pages 81-86

      The Finite Representability of \(J_{T_0 }\) and the Diagonal Space \(D \left( {\mathfrak{X}_\gamma } \right)\)

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      Book Chapter

      Pages 87-98

      The Spaces of Operators \(L\left( {\mathfrak{X}_\gamma } \right)\) , \(L\left( {X,\mathfrak{X}\omega _1 } \right)\)

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      Book Chapter

      Pages 99-103

      Transfinite Schauder Basic Sequences

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      Book Chapter

      Pages 105-116

      The Proof of the Finite Representability of \(J_{T_0 }\)

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      Book Chapter

      Pages 117-120

      Bibliography

  2. High-Dimensional Ramsey Theory and Banach Space Geometry

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      Book Chapter

      Pages 123-126

      Introduction

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      Book Chapter

      Pages 127-141

      Finite-Dimensional Ramsey Theory: Finite Representability of Banach Spaces

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      Book Chapter

      Pages 143-196

      Ramsey Theory of Finite and Infinite Sequences

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      Book Chapter

      Pages 197-216

      Ramsey Theory of Finite and Infinite Block Sequences

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      Book Chapter

      Pages 217-246

      Approximate and Strategic Ramsey Theory of Banach Spaces

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      Book Chapter

      Pages 247-252

      Bibliography