Introduction to Tensor Products of Banach Spaces
This book is intended as an introduction to the theory of tensor products of Banach spaces. The prerequisites for reading the book are a first course in Functional Analysis and in Measure Theory, as far as the Radon-Nikodym theorem. The book is entirely s
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Springer-Verlag London Ltd.
Raymond A. Ryan
Introduction to Tensor Products of Banach Spaces With 31 Figures
~Springer
Raymond A. Ryan
Department of Mathematics National University oflreland, Galway Galway Ireland
British Library Cataloguing in Publication Data Ryan, Raymond A. Introduction to tensor products of Banach spaces. (Springer monographs in mathematics) l. Banach spaces 2. Tensor products !.Title 515.7'32 ISBN 978-1-84996-872-0 Library of Congress Cataloging-in-Publication Data Ryan, Raymond A. Introduction to tensor products of Banach spaces I Raymond A. Ryan. p. em. -- (Springer monographs in mathematics) Includes bibliographical references and index. ISBN 978-1-84996-872-0 ISBN 978-1-4471-3903-4 (eBook) DOI 10.1007/978-1-4471-3903-4 l. Banach spaces 2. Tensor products. I. Title. II. Series. QA322.2.R92 2002 515'.732-dc21 2001049821 Mathematics Subject Classification (2000): 46-01,47-01, 46A32, 46B22, 46B28, 46M05, 47B10 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 licences issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. Springer Monographs in Mathematics JSSN 1439-7382 ISBN 978-1-84996-872-0 http://www.springer.co.uk ©Springer-Verlag London 2002 Originally published by Springer-Verlag London Berlin Heidelberg 2002 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. Typesetting: Camera-ready by the author 12/3830-543210 Printed on acid-free paper SPIN 10792170
To my parents
Preface
This book is intended as an introduction to the theory of tensor products of Banach spaces. The prerequisites for reading the book are a first course in Functional Analysis and in Measure Theory, as far as the Radon-Nikodym theorem. The book is entirely self-contained and two appendices give additional material on Banach Spaces and Measure Theory that may be unfamiliar to the beginner. No knowledge of tensor products is assumed. Our viewpoint is that tensor products are a natural and productive way to understand many of the themes of modern Banach space theory and that "tensorial thinking" yields insights into many otherwise mysterious phenomena. We hope to convince the reader of the validity of this belief. We begin in Chapter 1 with a treatment of the purely algebraic theory of tensor products
