Lp-Structure in Real Banach Spaces
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613 E. Behrends R. Danckwerts R. Evans S. Gobel P. Greim K. Meyfarth W. MUlier
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L -Structure in Real Banach Spaces
SpringerVeriag Berlin Heidelberg NewYork 1977
Authors Ehrhard Behrends Rainer Danckwerts Richard Evans Silke Gobel Peter Greim Konrad Meyfarth Winfried Muller
I. Mathematisches Institut der Freien Universitat Berlin Huttenweq 9 1000 Berlin 33/BRD
AMS Subject Classifications (1970): XX-46 ISBN 3-540-08441-X Springer-Verlag Berlin Heidelberg New York ISBN 0-387-08441-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
CON
TEN
T S
Introduction
Chapter 0: Preliminaries
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Chapter 1: LP-Projections Cet ouvrage vous est prete jusqu'au
Chapter 2: The Cunningham p-Algebra Chapter 3: The Integral Module Representation Chapter 4: The Classical LP-Spaces
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Chapter 5: Integral Modules and Duality pour autant que nous n'en ayons pas besoin pour la bibliotMquA ou pour un tiers.
Chapter 6: Spectral Theory for LP-Operators Chapter 7: The LP-Structure of the Bochner S1 and Related Results Appendix 1· The Commutativity of LP-Projecti oo
Appendix 2: L -Summands in CK-Spaces Appendix 3: A Measure-Theoretical Approach t Integral Modules
Notation Index Subject Index References
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Introduction In 1972, Alfsen and Effros ([AE1) pUblished a paper in which they discussed certain problems concerning the isometrical structure of Banach spaces. Using this paper as a starting point, a research group at the Freie Universitat Berlin has been working on structural problems of this type since the spring of 1973. During this period the results achieved by the group have been pUblished as papers, theses, and preprints. The purpose of these notes is to give the reader a more or less complete account of those results which can be grouped under the heading "LP-structure tt Let X be a real Banach space and 1
P
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00.
Two closed subspaces J,
of X are called com
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