Amenability (Mathematical Surveys and Monographs)

473 Pages·1988·4.59 MB·English

by  Alan L. T. Paterson

Amenability
Alan L. T. Paterson
American Mathematical Society
MATHEMATICAL SURVEYS
AND MONOGRAPHS SERIES LIST
Volume
I The problem of moments, 16 Symplectic groups,
J. A. Shohat and J. D. Tamarkin 0. Timothy O'Meara
2 The theory of rings, 17 Approximation by polynomials
N. Jacobson with integral coefficients,
Le Baron O. Ferguson
3 Geometry of polynomials,
M. Marden 18 Essentials of Brownian motion
and diffusion, Frank B. Knight
4 The theory of valuations,
O. F. G. Schilling 19 Contributions to the theory of
5 The kernel function and transcendental numbers, Gregory
V. Chudnovsky
conformal mapping,
S. Bergman 20 Partially ordered abelian groups
with interpolation, Kenneth R.
6 Introduction to the theory of
Goodearl
algebraic functions of one
variable, C. C. Chevalley 21 The Bieberbach conjecture:
Proceedings of the symposium on
7.1 The algebraic theory of
the occasion of the proof, Albert
semigroups, Volume 1, A. H.
Baernstein, David Drasin, Peter
Clifford and G. B. Preston
Duren, and Albert Marden,
7.2 The algebraic theory of
Editors
semigroups, Volume II, A. H.
22 Noncommutative harmonic
Clifford and G. B. Preston
analysis, Michael E. Taylor
8 Discontinuous groups and
23 Introduction to various aspects of
antomorphic functions,
degree theory in Banach spaces,
J. Lehner
E. H. Rothe
9 Linear approximation,
24 Noetherian rings and their
Arthur Sard
applications, Lance W. Small,
10 An introduction to the analytic
Editor
theory of numbers, R. Ayoub
25 Asymptotic behavior of dissipative
1i Fixed points and topological
systems, Jack K. Hale
degree in nonlinear analysis,
26 Operator theory and arithmetic in
J. Cronin
H°O, Hari Bercovici
12 Uniform spaces, J. R. Isbell
27 Basic hypergeometric series and
13 Topics in operator theory,
applications, Nathan J. Fine
A. Brown, R. G. Douglas,
28 Direct and inverse scattering on
C. Pearcy, D. Samson, A. L.
the lines, Richard Beals, Percy
Shields; C. Pearcy, Editor
Deift, and Carlos Tomei
14 Geometric asymptotics,
V. Guillemin and S. Sternberg
15 Vector measures, J. Diestel and
J. J. Uhl, Jr.

Amenability

Mathematical
Surveys
and
Monographs
Volume 29
Amenability
Alan L.T. Paterson
American Mathematical Society
Providence, Rhode island
2000 Mathematics Subject Classification. Primary 43-02, 43A07, 47H10,
22D25, 22D40, 22E15, 22E25, 03E10; Secondary 03E25, 20F05, 20F16,
20F18, 20F19, 20F24, 22D10, 22D15, 22E27, 28C15, 28D05, 43A60,
43A65, 43A80, 46H05, 46H25, 46J10, 46L05, 46L10, 47A35, 53C42,
54D35, 60B05, 60G50, 62F03.
Library of Congress Cataloging-In-Publication Data
Paterson, Alan L. T., 1944-
Amenability.
(Mathematical surveys and monographs; no. 29)
Includes bibliographies and Index.
1. Harmonic analysis. 2. Locally compact groups. I. Title. It. Series.
QA403.P37 1988 515'.2433 88-14485
ISBN 0-8218-1629-6 (als. paper)
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Copyright © 1988 by the American Mathematical Society
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1098765432 0403020100
Dedicated
to
MARLON M. DAY
Nicht die Neugierde, nicht die Eitelkeit, nicht die Betrachtung
der Nutzlichkeit, nicht die Pflieht and Gewiesenhaftigkeit, sondern
ein unaueloschlicher, ungliicklicher Durst, der sick auf keinen
Vergleich enldsst, fuhrt uns zur Wahrheit.
G. W. F. Hegel

Contents
Preface xi
List of Further Results xv
Plan xvii
CHAPTER 0. Introduction: Basic Concepts and Problems of Amenability
Theory 1
CHAPTER 1. Amenable Locally Compact Groups and Amenable
Semigroups 25
CHAPTER 2. The Algebra of Invariant Means 51
CHAPTER 3. Free Groups and the Amenability of Lie Groups 95
CHAPTER 4. Folner Conditions 125
CHAPTER 5. Ergodic Theorems for Amenable Locally Compact Groups 195
CHAPTER 6. Locally Compact Groups of Polynomial Growth 217
CHAPTER 7. Sizes of Sets of Invariant Means 269
APPENDICES:
A. Nilpotent, Solvable and Semidirect Product Groups 301
B. Lie Groups 305
C. Existence of Borel Cross-Sections 329
D. Mycielski's Theorem 331
E. On the Density of the Exponential Map 333
Some Abbreviations 337
Bibliography 339
Supplementary Bibliography ((S]) 397
Sketched Solutions to Problems 413
Index of Terms 443
Index of Symbols 451
ix