Non-commutative Gelfand Theories A Tool-kit for Operator Theorists a
Written as a hybrid between a research monograph and a textbook the first half of this book is concerned with basic concepts for the study of Banach algebras that, in a sense, are not too far from being commutative. Essentially, the algebra under consider
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Steffen Roch r Pedro A. Santos Bernd Silbermann
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Non-commutative Gelfand Theories A Tool-kit for Operator Theorists and Numerical Analysts
Steffen Roch Technische Universität Darmstadt Fachbereich Mathematik Schloßgartenstraße 7 64289 Darmstadt Germany [email protected]
Prof. Bernd Silbermann Technische Universität Chemnitz Fakultät für Mathematik Reichenhainer Straße 39 09126 Chemnitz Germany [email protected]
Pedro A. Santos Universidade Técnica de Lisboa Instituto Superior Técnico Departamento de Matemática Av. Rovisco Pais, 1 1049-001 Lisboa Portugal [email protected] Editorial board: Sheldon Axler, San Francisco State University Vincenzo Capasso, Università degli Studi di Milano Carles Casacuberta, Universitat de Barcelona Angus J. Macintyre, Queen Mary, University of London Kenneth Ribet, University of California, Berkeley Claude Sabbah, CNRS, École Polytechnique Endre Süli, University of Oxford Wojbor Woyczynski, Case Western Reserve University ISBN 978-0-85729-182-0 e-ISBN 978-0-85729-183-7 DOI 10.1007/978-0-85729-183-7 Springer London Dordrecht Heidelberg New York British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Mathematics Subject Classification (2010): 45E05, 45E10, 46H10, 46N20, 46N40, 47A53, 47B35, 65R20 © Springer-Verlag London Limited 2011 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licenses issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. The use of registered names, trademarks, etc., in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant laws and regulations and therefore free for general use. The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. Cover design: deblik Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Dedicated to the memory of Israel Gohberg (1928–2009).
Preface
The central notion in this book is that of a local principle. Local principles provide an abstract frame for the natural and extremely useful idea of localization, i.e. to divide a global problem into a family of local problems. The local principles the reader will encounter in this text are formulated in the language of Banach algebras and can be characterized as non-commutative Gelfand theories. They now form an integral part of the theory o
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