Noncommutative Stationary Processes
Quantum probability and the theory of operator algebras are both concerned with the study of noncommutative dynamics. Focusing on stationary processes with discrete-time parameter, this book presents (without many prerequisites) some basic problems of int
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Rolf Gohm
Noncommutative Stationary Processes
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Author Rolf Gohm Ernst-Moritz-Arndt University of Greifswald Department of Mathematics and Computer Science Jahnstr. 15a 17487 Greifswald Germany e-mail: [email protected]
Cataloging-in-Publication Data applied for Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at http://dnb.ddb.de
Mathematics Subject Classification (2000): 46L53, 46L55, 47B65, 60G10, 60J05 ISSN 0075-8434 ISBN 3-540-20926-3 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, specif ically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microf ilm 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 is a part of Springer Science + Business Media http://www.springeronline.com c Springer-Verlag Berlin Heidelberg 2004 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 specif ic 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 authors SPIN: 10983744
41/3142/du - 543210 - Printed on acid-free paper
Preface
Research on noncommutative stationary processes leads to an interesting interplay between operator algebraic and probabilistic topics. Thus it is always an invitation to an exchange of ideas between different fields. We explore some new paths into this territory in this book. The presentation proceeds rather systematically and elaborates many connections to already known results as well as some applications. It should be accessible to anyone who has mastered the basics of operator algebras and noncommutative probability but, concentrating on new material, it is no substitute for the study of the older sources (mentioned in the text at appropriate places). For a quick orientation see the Summary on the following page and the Introduction. There are also additional introductions in the beginning of each chapter. The text is a revised version of a manuscript entitled ‘Elements of a spatial theory for noncommutative stationary processes with discrete time index’, which has been written by the author as a habilitation thesis (Greifswald, 2002). It is impossible to give a complete picture of all the mathematical influences on me which shaped this work. I want to thank all who have been
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