Geometric Aspects of Functional Analysis: Israel Seminar (GAFA) 1987-88

ISBN-13: 9783540513032 / Angielski / Miękka / 1989 / 292 str.

Joram Lindenstrauss;Vitali D. Milman

Opis

This volume contains a collection of original research papers on recent developments in Banach space theory and related areas by many of the leading research workers in the field. A considerable number of papers are devoted to structure theory of infinite-dimensional Banach spaces. This research ground has experienced a remarkable breakthrough in recent years, which has given new insight into infinite-dimensional geometry (even of Hilbert spaces). Several new results and examples are included in this volume and new research directions are surveyed. Other contributions concern the well established local theory of Banach spaces and its fruitful connection with classical convexity in Rn. The volume also contains several papers on harmonic analysis, probabilistic methods in functional analysis and nonlinear geometry. Research workers and graduate students in Banach space theory, convexity, harmonic analysis and probability will value this book's utility and insight.

Spis treści

Hilbert's 13th problem and dimension.- On the duality problem for entropy numbers of operators.- Isotropic position and inertia ellipsoids and zonoids of the unit ball of a normed n-dimensional space.- An “isomorphic” version of the sauer-shelah lemma and the banach-mazur distance to the cube.- On complemented subspaces of H 1 and VMO.- An approximation theorem for vector valued functions.- Geometry of finite dimensional subspaces and quotients of L p.- Estimates of bernstein widths of sobolev spaces.- Probabilistic proofs of existence of rare events.- On the behavior of the constant in the littlewood-paley inequality.- On kolmogorov's rearrangement problem for orthogonal systems and garsia's conjecture.- Volumes of sections of cubes and related problems.- On santaló's inequality.- Estimates related to steiner symmetrizations.- A remark concerning the dependence on ? in dvoretzky's theorem.- Almost euclidean sections in spaces with a symmetric basis.