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This treatment of analysis on semigroups stresses the functional analytical and dynamical theory of continuous representations of semitopological semigroups. Topics covered include compact semitopological semigroups, invariant means and idempotent means on compact semitopological semigroups, affine compactifications, left multiplicatively continuous functions and weakly left continuous functions, compactifications of infinite direct products, and weakly almost periodic semigroups of Markov operators. Contains over 200 exercises, from simple applications and examples to further developments of the theory.
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Analysis On Semigroups CANADIAN MATHEMATICAL SOCIETY SERIES OF MONOGRAPHS AND ADVANCED TEXTS Monographies et Etudes de laiSociété Mathe’matique du Canada EDITORIAL BOARD Frederick V. Atkinson, Bernhard Banaschewski, Colin W. Clark, Erwin O. Kreyszig (Chairman) and John B. Walsh \31 Frank H. Clarke Optimization and Nonsmooth Analysis Erwin Klein and Anthony C. Thompson Theory of Correspondences: Including Applications to Mathematical Economics I. Gohberg, P. Lancaster, and L. Rodman Invariant Subspaces ofMotrices with Applications Jonathan Borwein and Peter Borwein PI and the AGM—A Study in Analytic Number Theory and Computational Complexity Subhashis Nag The Complex Analytic Theory of Teichmt'iller Spaces Erwin Kreyszig and Manfred Kracht Methods of Complex Analysis in Partial Difirerential Equations with Applications Ernst J. Kani and Robert A. Smith The Collected Papers of Hans Arnold Heilbronn John F. Berglund, Hugo D. Junghenn, and Paul Milnes Analysis on Semigroups: Function Spaces, Compactifications, Representations Victor P. Snaith Topological Methods in Galois Representation Theory Kalathoor Varadarajan The Finiteness Obstruction of C. T. C. Wall Analysis on Semigroups Function Spaces, Compactifications, Representations JOHN F. BERGLUND Virginia Commonwealth University, Richmond HUGO D. JUNGHENN George Washington University, Washington, D. C. PAUL MILNES The University of Western Ontario, London, Canada WILEY A Wiley-Interscience Publication JOHN WILEY & SONS New York ° Chichéster - Brisbane - Toronto - Singapore Copyright © 1989 by John Wiley & Sons, Inc. All rights reserved. Published simultaneously in Canada. Reproduction or translation of any part of this work beyond that permitted by Section 107 or 103 of the 1976 United Slates Copyright Act without the permission of the copyright owner is unlawful. Requests for permission or further information should be addressed to the Permissions Department, John Wiley & Sons, Inc. Library of Congress Cataloging-in-Publicarion Data Berglund, John F. Analysis on semigroups: function spaces, compactifications, representations/by John F. Berglund, Hugo D. Junghenn, Paul Milnes. p. cm.—(Canadian Mathematical Society series of monographs and advanced texts = Monographies et études de la Société mathématique du Canada) “A Wiley—Interscience publication. ” Bibliography: p. Includes indexes. ISBN 0—471—61208-1 l. Topological semigroups. 2. Representations of semigroups. 3. Bohr compactification. I. Junghenn. Hugo D. II. Milnes. Paul. III. Title. IV. Series: Canadian Mathematical Society series of monographs and advanced texts. QA387.B47 1988 512'.55—dcl9 . _ Printed in the United States of Amenca 10987654321 88-14292 CIP T0 the memory of Vicki Ostrolenk, loving wife, devoted friend Preface This book presents a unified treatment of certain topics in analysis on semigroups, in particular, those topics that pertain to the functional analytic and dynamical theory of continuous representations of semitopological semigroups. It is well kn