Operator Algebras Generated by Commuting Projections: A Vector Measure Approach
This book presents a systematic investigation of the theory of those commutative, unital subalgebras (of bounded linear operators acting in a Banach space) which are closed for some given topology and are generated by a uniformly bounded Boolean algebra o
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1711
Lecture Notes in Mathematics Editors: A. Dold, Heidelberg F. Takens, Groningen B. Teissier, Paris
1711
Springer Berlin Heidelberg New York Barcelona Hong Kong London Milan Paris Singapore Tokyo
Werner Ricker
Operator Algebras Generated by Commuting Projections: AVector Measure Approach
Springer
Author Werner Ricker School of Mathematics University of New South Wales Sydney, NSW, 2052 Australia e-mail: [email protected] Cataloging-in-Publication Data applied for
Die Deutsche Bibliothek - CIP-Einheitsaufnahme
Ricker, Werner: Operator algebras generated by commuting projections: a vector measure approach / Werner Ricker. - Berlin; Heidelberg; New York ; Barcelona; Hong Kong; London; Milan; Paris; Singapore; Tokyo: Springer, 1999 (Lecture notes in mathematics; 1711) ISBN 3-540-66461-0
Mathematics Subject Classification (1991): 28B05, 06E15, 47B40, 47D30 ISSN 0075-8434 ISBN 3-540-66461-0 Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1999 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Camera-ready TEX output by the author SPIN: 10700204 41/3143-543210 - Printed on acid-free paper
For Margit, Simon and Sandra; without their constant encouragement and support these notes would never have eventuated.
PREFACE In the summer semester of 1997 Professor Jim Cooper invited me to give an advanced set of lectures at the Honours/Masters level in the Mathematisches Institut of the Johannes Kepler Universitat in Linz, Austria. He left the choice of topic up to me; his only request was that the topic should be of an interdisciplinary nature since the students already had a good background in such individual courses as algebra, linear algebra, real and complex analysis, functional analysis and measure theory, etc.. The content of this book is essentially an expanded version of the lectures given in Linz. The material was chosen in an attempt to illustrate to advanced students that it is indeed possible to present lecture courses within their mathematical reach which form a connecting bridge between many of the specialized courses that they have already had and such that it "all comes together." In addition to being able to absorb a body of math
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