Integrals and Operators
TO THE SECOND EDITION Since publication of the First Edition several excellent treatments of advanced topics in analysis have appeared. However, the concentration and penetration of these treatises naturally require much in the way of technical preliminar
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Editors
S. S. Chern J. L. Doob J. Douglas, jr. A. Grothendieck E. Heinz F. Hirzebruch E. Hopf S. Mac Lane W. Magnus M. M. Postnikov W. Schmidt D. S. Scott K. Stein J. Tits B. L. van der Waerden Managing Editors
B. Eckmann J. K. Moser
Irving E. Segal Ray A. Kunze
Integrals and Operators Second Revised and Enlarged Edition
Springer-Verlag Berlin Heidelberg New York 1978
Irving E. Segal Massachusetts Institute of Technology, Cambridge, MA 02139, USA Ray A. Kunze University of California at Irvine, Irvine, CA 92664, USA
First edition © 1968 by McGraw-Hill, Inc.
AMS Subject Classifications (1970): 22 B xx, 22 C 05,22 D xx, 28-XX, 43-XX, 46-XX, 47-XX
ISBN-13: 978-3-642-66695-7 DOl: 10.1007/978-3-642-66693-3
e-ISBN-13: 978-3-642-66693-3
Library of Congress Cataloging in Publication Data. Segal, Irving Ezra. Integrals and operators (Grundlehren der mathematischen Wissenschaften; 228). Bibliography: p. Includes index. I. Integrals, Generalized. 2. Functional analysis. I. Kunze, Ray Alden, 1928-joint author. II. Title. III. Series: Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen; 228. QA312.S4. 1978. 515'.42. 77-16682 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. © by Springer-Verlag Berlin Heidelberg 1978
Softcover reprint of the hardcover 2nd edition 1978 2141/3140-543210
PREFACE TO THE SECOND EDITION
Since publication of the First Edition several excellent treatments of advanced topics in analysis have appeared. However, the concentration and penetration of these treatises naturally require much in the way of technical preliminaries and new terminology and notation. There consequently remains a need for an introduction to some of these topics which would mesh with the material of the First Edition. Such an introduction could serve to exemplify the material further, while using it to shorten and simplify its presentation. It seemed particularly important as well as practical to treat briefly but cogently some of the central parts of operator algebra and higher operator theory, as these are presently represented in book form only with a degree of specialization rather beyond the immediate needs or interests of many readers. Semigroup and perturbation theory provide connections with the theory of partial differential equations. C*-algebras are important in harmonic analysis and the mathematical foundations of quantum mechanics. W*-algebras (or von Neumann rings) provide an approach to the theory of multiplicity of the spectrum and some simple but key elements of the grammar of analysis, of use in group representation theory and elsewhere. The v
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Preface
