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Asymptotic Theory of Finite Dimensional Normed Spaces

Isoperimetric Inequalities in Riemannian Manifolds

  • Book
  • © 1986

Overview

Authors:
  1. Vitali D. Milman

    1. Department of Mathematics, Tel Aviv University, Ramat Aviv, Israel

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  2. Gideon Schechtman

    1. Department of Theoretical Mathematics, The Weizmann Institute of Science, Rehovot, Israel

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  • Reprinted because of continuing demand

Part of the book series: Lecture Notes in Mathematics (LNM, volume 1200)

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Table of contents (15 chapters)

  1. Front Matter

    Pages I-X
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  4. Back Matter

    Pages 114-156
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Keywords

About this book

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 distances between finite dimensional normed spaces are studied in detail. Another related book is Pietch's [Pie].

Authors and Affiliations

  • Department of Mathematics, Tel Aviv University, Ramat Aviv, Israel

    Vitali D. Milman

  • Department of Theoretical Mathematics, The Weizmann Institute of Science, Rehovot, Israel

    Gideon Schechtman

Bibliographic Information

  • Book Title: Asymptotic Theory of Finite Dimensional Normed Spaces

  • Book Subtitle: Isoperimetric Inequalities in Riemannian Manifolds

  • Authors: Vitali D. Milman, Gideon Schechtman

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-3-540-38822-7

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1986

  • Softcover ISBN: 978-3-540-16769-3Published: 01 July 1986

  • eBook ISBN: 978-3-540-38822-7Published: 27 February 2009

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XII, 160

  • Topics: Analysis, Convex and Discrete Geometry

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