Geometric Aspects of Functional Analysis

Chapter 1 ψ 2 -Estimate for the Euclidean Norm on a Convex Body in Isotropic Position

Chapter 2 Embedding ℓ ∞ n -Cubes in Low Dimensional Schatten Classes

Chapter 3 Products of Unconditional Bodies

Chapter 4 Remarks on Halasz-Montgomery Type Inequalities

Chapter 5 Estimates for Cone Multipliers

Chapter 6 Remarks on Bourgain’s Problem on Slicing of Convex Bodies

Chapter 7 A Note on the Banach-Mazur Distance to the Cube

Chapter 8 Projection Functions on Higher Rank Grassmannians

Chapter 9 On the Volume of Unions and Intersections of Balls in Euclidean Space

Chapter 10 Uniform Non-Equivalence between Euclidean and Hyperbolic Spaces

Chapter 11 A Hereditarily Indecomposable Space with an Asymptotic Unconditional Basis

Chapter 12 Proportional Subspaces of Spaces with Unconditional Basis Have Good Volume Properties

Chapter 13 A Remark about Distortion

Chapter 14 Symmetric Distortion in ℓ 2

Chapter 15 Asymptotic Infinite-Dimensional Theory of Banach Spaces

Chapter 16 On the Richness of the Set of p ’s in Krivine’s Theorem

Chapter 17 Kolmogorov’s Theorems in Fourier Analysis

Chapter 18 Two Unexpected Examples Concerning Differentiability of Lipschitz Functions on Banach Spaces

Chapter 19 Determinant Inequalities with Applications to Isoperimatrical Inequalities

Chapter 20 Approximate John’s Decompositions

Chapter 21 Two Remarks on 1-Unconditional Basic Sequences in L p , 3 ≤ p < ∞

Chapter 22 A Concentration Inequality for Harmonic Measures on the Sphere

Chapter 23 A Concentration of Measure Phenomenon on Uniformly Convex Bodies

Chapter 24 Embedding of ℓ k ∞ and a Theorem of Alon and Milman

Chapter 25 Are All Sets of Positive Measure Essentially Convex?

Chapter 26 Embedding Subspaces of L p in ℓ p N

Chapter 27 Distortions on Schatten Classes Cp