Banach Spaces of Continuous Functions as Dual Spaces
This book gives a coherent account of the theory of Banach spaces and Banach lattices, using the spaces C_0(K) of continuous functions on a locally compact space K as the main example. The study of C_0(K) has been an important area of functional analysis
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H.G. Dales F.K. Dashiell, Jr. A.T.-M. Lau D. Strauss
Canadian Mathematical Society Société mathématique du Canada
Banach Spaces of Continuous Functions as Dual Spaces
Canadian Mathematical Society Société mathématique du Canada Editors-in-Chief Rédacteurs-en-chef K. Dilcher K. Taylor Advisory Board Comité consultatif M. Barlow H. Bauschke L. Edelstein-Keshet N. Kamran M. Kotchetov
More information about this series at http://www.springer.com/series/4318
H.G. Dales • F.K. Dashiell, Jr. A.T.-M. Lau • D. Strauss
Banach Spaces of Continuous Functions as Dual Spaces
123
H.G. Dales Department of Mathematics and Statistics University of Lancaster Lancaster, UK
F.K. Dashiell, Jr. Center of Excellence in Computation Algebra, and Topology (CECAT) Chapman University Orange, CA, USA
A.T.-M. Lau Department of Mathematical Sciences University of Alberta Edmonton, AB, Canada
D. Strauss Department of Pure Mathematics University of Leeds Leeds, UK
ISSN 1613-5237 CMS Books in Mathematics ISBN 978-3-319-32347-3 DOI 10.1007/978-3-319-32349-7
ISSN 2197-4152 (electronic) ISBN 978-3-319-32349-7 (eBook)
Library of Congress Control Number: 2016937361 Mathematics Subject Classification (2010): 46-02, 46B03, 46B04, 46B10, 46B22, 46B25, 46B42, 28A33, 28A60, 46L05, 46L10 © Springer International Publishing Switzerland 2016 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 omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
This volume is dedicated to the memory of William G. Bade 29 May, 1924–10 August, 2012 with our affection and respect.
Preface
Let K be a locally compact space, and denote by C0 (K) the Banach space of all continuous functions on K that vanish at infinity, taken with the uniform norm. This fundamentally important and very familiar Banach space has been studied for many decades, and it arises in a va
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