Asymptotic Theory of Finite Dimensional No...

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Sprache: Englisch

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Beschreibung

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].

Zusammenfassung

Reprinted because of continuing demand

Inhaltsverzeichnis

The Concentration of Measure Phenomenon in the Theory of Normed Spaces.- Preliminaries.- The Isoperimetric Inequality on Sn?1 and Some Consequences.- Finite Dimensional Normed Spaces, Preliminaries.- Almost Euclidean Subspaces of A Normed Space.- Almost Euclidean Subspaces of ?{p}n Spaces, of General n-Dimensional Normed Spaces, and of Quotient of n-Dimensional Spaces.- Levy Families.- Martingales.- Embedding ?pm into ?1n.- Type and Cotype of Normed Spaces, and Some Simple Relations with Geometrical Properties.- Additional Applications of Levy Families in the Theory of Finite Dimensional Normed Spaces.- Type and Cotype of Normed Spaces.- Ramsey's Theorem with Some Applications to Normed Spaces.- Krivine's Theorem.- The Maurey-Pisier Theorem.- The Rademacher Projection.- Projections on Random Euclidean Subspaces of Finite Dimensional Normed Spaces.

Erscheinungsjahr:	1986
Fachbereich:	Geometrie
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Seiten:	172
Reihe:	Lecture Notes in Mathematics
Inhalt:	xii 160 S.
ISBN-13:	9783540167693
ISBN-10:	3540167692
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Schechtman, Gideon Milman, Vitali D.
Auflage:	1986
Hersteller:	Springer-Verlag GmbH Springer Berlin Heidelberg Lecture Notes in Mathematics
Maße:	235 x 155 x 10 mm
Von/Mit:	Gideon Schechtman (u. a.)
Erscheinungsdatum:	01.07.1986
Gewicht:	0,271 kg

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