Ramsey Methods in Analysis

"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

• 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.