Ramsey Methods in Analysis

• Κύριοι συγγραφείς: Argyros, Spiros A. (Συγγραφέας), Todorcevic, Stevo (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Basel : Birkhäuser Basel, 2005.
• Σειρά: Advanced Courses in Mathematics CRM Barcelona, Centre de Recerca Matemática
• Θέματα: Mathematics.; Functional analysis.; Combinatorics.; Functional Analysis.

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,...

Πίνακας περιεχομένων:

• Saturated and Conditional Structures in Banach Spaces
• Tsirelson and Mixed Tsirelson Spaces
• Tree Complete Extensions of a Ground Norm
• Hereditarily Indecomposable Extensions with a Schauder Basis
• The Space of the Operators for Hereditarily Indecomposable Banach Spaces
• Examples of Hereditarily Indecomposable Extensions
• The Space $$\mathfrak{X}\omega _1 $$
• The Finite Representability of $$J_{T_0 }$$ and the Diagonal Space $$D \left( {\mathfrak{X}_\gamma } \right)$$
• The Spaces of Operators $$L\left( {\mathfrak{X}_\gamma } \right)$$ , $$L\left( {X,\mathfrak{X}\omega _1 } \right)$$
• Transfinite Schauder Basic Sequences
• The Proof of the Finite Representability of $$J_{T_0 }$$
• High-Dimensional Ramsey Theory and Banach Space Geometry
• Finite-Dimensional Ramsey Theory: Finite Representability of Banach Spaces
• Ramsey Theory of Finite and Infinite Sequences
• Ramsey Theory of Finite and Infinite Block Sequences
• Approximate and Strategic Ramsey Theory of Banach Spaces.