Induced Representations and Banach *-Algebraic Bundles with an Appen
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582 J. M. G. Fell
Induced Representations and Banach *-Algebraic Bundles with an Appendix due to A. Douady and L. Dal Soglio-Herault
Springer-Verlag Berlin. Heidelberg • New York 1977
Author
J. M. G. Fell Department of Mathematics, University of Pennsylvania Philadelphia, PA 19174/USA
Library of Congress Cataloging in Publication Data
Fell, James Michael Gardner, 1923~ Induced representations aad Bsmach *-algebraic bundles. (Lecture notes in mathematics ; 582) Bibliography: p. Includes index, 1. Locally compact groups. 42 , Representation~ of groups. 3- Banaeh algebras. . C*= algebras. I, Title. II, Series : Lecture notes in mathematics (Berlin) ; 582. QA3.L28 no. 582 [qA387]
510'.8s [512'.55]
77-5113
AMS Subject Classifications (1970): 22D10, 22D30, 43A65, 46H15, 46H25, 46 K10, 46L05 ISBN 3-540-08147-X Springer-Verlag Berlin • Heidelberg • New York ISBN 0-387-08147-X Springer-Verlag New York • Heidelberg • Berlin 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 1977 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2141/3140-543210
TABLE OF CONTENTS Page 1
Introduction CHAPTER
I:
THE ABSTRACT INDUCING IMPRIMITIVITY
PROCESS AND ABSTRACT
§i.
Operator
inner products
§2.
Duality
§3.
Hermitian modules
§4.
Rigged modules
95.
General
§6.
The regional topology of representations of the inducing process
97.
Imprimitivity
§8.
The abstract
§9.
Topological versions and examples Imprimitivity Theorem
for operator
II:
inner products
36 43
and the abstract
properties
CHAPTER
28
of abstract
inducing process induction
54 and the continuity
bimodules Imprimitivity
BANACH
Theorem
*-ALGEBRAIC
81 of the abstract
99
*-algebraic
bundles
112 125
§13. The cross-sectional
algebra
133
*-Representations
915. The integrated §16. Positive
87
BUNDLES
§12. Examples
§14.
60 72
§i0. Banach bundles §ii. Banach
47
140
form of a *-representation
functionals
§17. When do enough
on the cross-sectional
*-representations
150 algebra
exist?
153 160
§18. The bundle C * - c o m p l e t i o n
168
§19. Bundle
172
structures
§20. The regional
for C*-algebras
topology
of *-representations
of bundles
179
C H A P T E R III:
INDUCED R E P R E S E N T A T I O N S AND I M P R I M I T I V I T Y FOR BANACH *-ALGEBRAIC BUNDLES
§21. The framework of the induction process in the bundle context. P o s i t i v i t y with respect to a Banach *-algebraic bundle
193
§22. E q u i v a l e n t
200
conditions
for p o s i t i v i t y
§23. The induced H i l b e r t bundle
207
§24. The action of
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