Geometric Aspects of Functional Analysis: Israel Seminar (GAFA) 1992–94(77 Operator Theory: Advances and Applications)

This volume contains a collection of original research papers on recent developments in Banach space theory and related areas. Many of the papers are devoted to structure theory of infinite-dimensional Banach spaces. Several new results are included and new research directions are surveyed. Other contributions concern the well-established local theory of Banach spaces and is connection with classical convexity. This volume also features several papers on harmonic analysis, probabilistic methods in functional analysis and non-linear geometry. It is intended for research workers and graduate students in Banach space theory, convexity, harmonic analysis and probability.

Table of Contents:
?2-estimate for the euclidean norm on a convex body in isotropic position.- References.- Embedding ?n?-Cubes in low dimensional Schatten classes.- References.- Products of unconditional bodies.- 0 Introduction.- 1 The general Lozanovskii problem for products of unconditional bodies.- 2 Volumes of products of unconditional bodies.- References.- Remarks on Halasz-Montgomery type inequalities.- 1 Introduction.- 2 Proof of Proposition 1.- 3 Proof of Proposition 2.- 4 Zero-density estimates.- References.- Estimates for cone multipliers.- 0 Summary.- 1 L4-estimates.- 2 Kakeya type structures.- 3 A first L2-estimate.- 4 Fourier transform of measures on a cone.- 5 Application to cone multipliers.- References.- Remarks on Bourgain’s problem on slicing of convex bodies.- References.- A note on the Banach-Mazur distance to the cube.- 1 Introduction.- 2 Proof of the Proposition.- 3 Remark.- References.- Projection functions on higher rank Grassmannians.- 1 Introduction.- 2 Projection functions and surface area measures.- 3 The sizes of projection classes.- 4 Radon transforms and projection functions.- References.- On the volume of unions and intersections of balls in Euclidean space.- 1 Introduction.- 2 Volume of flowers in Sn?1 and ?n.- 3 Extension to special cases of N caps in Sn?1.- References.- Uniform non-equivalence between Euclidean and hyperbolic spaces.- 1 Introduction.- 2 Necessary definitions.- 3 The big spheres tangency.- 4 One negative result.- 5 The results.- 6 The proofs.- References.- A hereditarily indecomposable space with an asymptotic unconditional basis.- 1 Introduction.- 2 Some definitions and basic lemmas.- 3 The definition of the space and some of its properties.- 4 Proof of the main result.- References.- Proportional subspaces of spaces withunconditional basis have good volume properties.- 1 Introduction.- 2 Proofs.- References.- A remark about distortion.- References.- Symmetric distortion in ?2.- 1 Symmetric ABS in ?2.- 2 The ?r case.- References.- Asymptotic infinite-dimensional theory of Banach spaces.- 1 Asymptotic and permissible spaces.- 2 Asymptotic versions.- 3 Uniqueness of the asymptotic-?p structure.- 4 Duality of asymptotic-?p spaces.- 5 Complemented permissible subspaces.- References.- On the richness of the set of p’s in Krivine’s theorem.- 1 A space with no spreading model containing c0 or ?p.- 2 A space with a large nonshrinkable Krivine-p-set.- References.- Kolmogorov’s theorems in Fourier analysis.- 0 Introduction.- 1 Kolmogorov’s example of divergent Fourier Series.- 2 Kolmogorov’s weak type inequality.- 3 Kolmogorov’s rearrangement theorem.- References.- Two unexpected examples concerning differentiability of Lipschitz functions on Banach spaces.- 1 Incompatibility of Gâteaux and Fréchet differentiability results.- 2 Strange difference between Fréchet differentiability of Lipschitz functions and of Lipschitz mappings.- References.- Determinant inequalites with applications to isoperimetric inequalities.- 1 Introduction.- 2 Determinant estimates.- 3 Infinite determinants.- 4 Isoperimetric inequalities for simplices.- References.- Approximate John’s decompositions.- References.- Two remarks on 1-unconditional basic sequences in Lp, 3 ? p < ?.- References.- A concentration inequality for harmonic measures on the sphere.- 1 Introduction and notation.- 2 The concentration inequality.- 3 Some corollaries of Theorem 2.1.- 4 Exit times for convex symmetric bodies.- 5 Appendix.- References.- A concentration of measure phenomenon on uniformly convex bodies.- 1Maurey’s proof.- 2 Uniform convex spaces.- 3 An estimate for the floating body of Bdp.- References.- Embedding of ??k and a theorem of Alon and Milman.- References.- Are all sets of positive measure essentially convex?.- 1 Introduction.- 2 Gauss space.- 3 Some aspects of the solid case.- 4 Sets of sequences.- References.- Embedding subspaces of Lp in ?Np.- 1 Introduction.- 2 The iteration method and the random choice.- 3 Tree extraction.- 4 Entropy estimates.- 5 Main construction.- References.- Distortions on Schatten classes Cp.- 1 Preliminary remarks.- 2 Asymptotic sets in Cp.- References.- GAFA Seminar — List of Talks.