Asymptotic Theory of Finite Dimensional Normed Spaces
This book deals with the geometrical structure of finite dimensional normed spaces, as the dimension grows to infinity. This is a part of what came to be known as the Local Theory of Banach Spaces (this name was derived from the fact that in its first sta
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Springer Berlin Heidelberg New York Barcelona Hong Kong London Milan Paris Singapore Tokyo
Vitali D. Milman Gideon Schechtman
Asymptotic Theory of Finite Dimensional Normed Spaces With an Appendix by M. Gromov "Isoperimetric Inequalities in Riemannian Manifolds"
Springer
Authors Vitali D. Milman Department of Mathematics Tel Aviv University Ramat Aviv, Israel Gideon Schechtman Department of Theoretical Mathematics The Weizmann Institute of Science Rehovot, Israel
Cataloging-in-Publication Data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme Milman, Vitali D.: Asymptotic theory of finite dimensional normed spaces / Vitali D. Milman; Gideon Schechtman. With an appendix Isoperimetric inequalities in Riemannian manifolds / by M. Gromov. - Corr. 2. printing. - Berlin; Heidelberg; New York; Barcelona; Hong Kong; London; Milan; Paris; Singapore; Tokyo: Springer, 2001 (Lecture notes in mathematics ; 1200) ISBN 3-540-16769-2
Corrected Second Printing 2001 Mathematics Subject Classification (1980): 46B20, 52A20, 60FlO ISSN 0075-8434 ISBN 3-540-16769-2 Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfi Ims or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. Springer-Verlag Berlin Heidelberg New York a member of BertelsmannSpringer Science+Business Media GmbH http://www.springer.de © Springer-Verlag Berlin Heidelberg 1986 Printed in Germany Typesetting: Camera-ready TEX output by the authors SPIN: 10797471 41/3142-543210 - Printed on acid-free paper
INTRODUCTION This book deals with the geometrical structure of finite dimensional normed spaces, as the dimension grows to infinity.
This is a part of what came to be known as the Local
Theory of Banach Spaces (this name was derived from the fact that in its first stages, this theory dealt mainly with relating the structure of infinite dimensional Banach spaces to the structure of their lattice of finite dimensional subspaces). Our purpose in this book is to introduce the reader to some of the results, problems, and mainly methods developed in the Local Theory, in the last few years. This by no means is a complete survey of this wide area. Some of the main topics we do not discuss here are mentioned in the Notes and Remarks section. Several books appeared recently or are going to appear shortly, which cover much of the material not covered in this book. Among these are Pisier's [Pis6] where factorization theorems related to Grothendieck's theorem are extensively discussed, and Tomczak-Jaegermann's [T-Jl] where operator ideals and
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