DYNAMICS OF INFINITE-DIMENSIONAL GROUPS by Vladimir Pestov ( 9780821841372 )

Item Details

Title:

DYNAMICS OF INFINITE-DIMENSIONAL GROUPS
THE RAMSEY-DVORETZKY-MILMAN PHENOMENON

By:

Format:

Paperback

List price:	£61.00
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ISBN 10:

0821841378

ISBN 13:

9780821841372

Publisher:

AMERICAN MATHEMATICAL SOCIETY

Pub. date:

15 December, 2006

Series:

University Lecture Series No. 40

Pages:

192

Description:

Refers to unitary groups of Hilbert spaces, the infinite symmetric group, groups of homeomorphisms of manifolds, and groups of transformations of measure spaces. This book presents an approach to the study of such groups based on ideas from geometric functional analysis and from exploring the interplay between dynamical properties of those groups.

Synopsis:

The ""infinite-dimensional groups"" in the title refer to unitary groups of Hilbert spaces, the infinite symmetric group, groups of homeomorphisms of manifolds, groups of transformations of measure spaces, etc. The book presents an approach to the study of such groups based on ideas from geometric functional analysis and from exploring the interplay between dynamical properties of those groups, combinatorial Ramsey-type theorems, and the phenomenon of concentration of measure. The dynamics of infinite-dimensional groups is very much unlike that of locally compact groups. For instance, every locally compact group acts freely on a suitable compact space (Veech). By contrast, a 1983 result by Gromov and Milman states that whenever the unitary group of a separable Hilbert space continuously acts on a compact space, it has a common fixed point. In the book, this new fast-growing theory is built strictly from well-understood examples up. The book has no close counterpart and is based on recent research articles. At the same time, it is organized so as to be reasonably self-contained.The topic is essentially interdisciplinary and will be of interest to mathematicians working in geometric functional analysis, topological and ergodic dynamics, Ramsey theory, logic and descriptive set theory, representation theory, topological groups, and operator algebras.

Illustrations:

Illustrations

Publication:

Imprint:

American Mathematical Society

Returns:

Returnable

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