Operator Theoretic Aspects of Ergodic Theory

Stunning recent results by Host–Kra, Green–Tao, and others, highlight the timeliness of this systematic introduction to classical ergodic theory using the tools of operator theory. Assuming no prior exposure to ergodic theory, this book provides a modern

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Tanja Eisner Bálint Farkas Markus Haase Rainer Nagel

Operator Theoretic Aspects of Ergodic Theory

Graduate Texts in Mathematics

272

Graduate Texts in Mathematics Series Editors: Sheldon Axler San Francisco State University, San Francisco, CA, USA Kenneth Ribet University of California, Berkeley, CA, USA

Advisory Board: Alejandro Adem, University of British Columbia David Eisenbud, University of California, Berkeley & MSRI Irene M. Gamba, The University of Texas at Austin J.F. Jardine, University of Western Ontario Jeffrey C. Lagarias, University of Michigan Ken Ono, Emory University Jeremy Quastel, University of Toronto Fadil Santosa, University of Minnesota Barry Simon, California Institute of Technology

Graduate Texts in Mathematics bridge the gap between passive study and creative understanding, offering graduate-level introductions to advanced topics in mathematics. The volumes are carefully written as teaching aids and highlight characteristic features of the theory. Although these books are frequently used as textbooks in graduate courses, they are also suitable for individual study.

More information about this series at http://www.springer.com/series/136

Tanja Eisner • Bálint Farkas • Markus Haase Rainer Nagel

Operator Theoretic Aspects of Ergodic Theory

123

Bálint Farkas School of Mathematics and Natural Sciences University of Wuppertal Wuppertal, Germany

Tanja Eisner Institute of Mathematics University of Leipzig Leipzig, Germany Markus Haase Department of Mathematics Kiel University Kiel, Germany

ISSN 0072-5285 ISBN 978-3-319-16897-5 DOI 10.1007/978-3-319-16898-2

Rainer Nagel Mathematical Institute University of Tübingen Tübingen, Germany

ISSN 2197-5612 (electronic) ISBN 978-3-319-16898-2 (eBook)

Library of Congress Control Number: 2015937747 Mathematics Subject Classification: 37-xx, 47-xx, 46-xx, 37Axx, 46B42 Springer Cham Heidelberg New York Dordrecht London © Tanja Eisner, Bálint Farkas, Markus Haase, and Rainer Nagel 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, 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. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omiss