Banach Space Theory The Basis for Linear and Nonlinear Analysis
Banach spaces provide a framework for linear and nonlinear functional analysis, operator theory, abstract analysis, probability, optimization and other branches of mathematics. This book introduces the reader to linear functional analysis and to related p
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ditors-in-Chief Rédacteurs-en-chef K. Dilcher K. Taylor
Advisory Board Comité consultatif G. Bluman P. Borwein R. Kane
For other titles published in this series, go to http://www.springer.com/series/4318
Marián Fabian · Petr Habala · Petr Hájek · Vicente Montesinos · Václav Zizler
Banach Space Theory The Basis for Linear and Nonlinear Analysis
123
Marián Fabian Mathematical Institute of the Academy of Sciences of the Czech Republic Žitná 25, Praha 1 11567 Prague, Czech Republic [email protected]
Vicente Montesinos Universidad Politécnica de Valencia Departamento de Matematica Aplicada Camino de Vera s/n 46022 Valencia, Spain [email protected]
Petr Habala Czech Technical University in Prague Department of Mathematics Faculty of Electrical Engineering Technická 2 16627 Prague, Czech Republic [email protected]
Václav Zizler University of Alberta Department of Mathematical and Statistical Sciences Central Academic Building Edmonton T6G 2G1 Alberta, Canada [email protected]
Petr Hájek Mathematical Institute of the Academy of Sciences of the Czech Republic Žitná 25, Praha 1 11567 Prague, Czech Republic [email protected] Editors-in-Chief Rédacteurs-en-chef Canada K. Dilcher K. Taylor Department of Mathematics and Statistics Dalhousie University Halifax, Nova Scotia B3H 3J5 [email protected]
ISSN 1613-5237 ISBN 978-1-4419-7514-0 e-ISBN 978-1-4419-7515-7 DOI 10.1007/978-1-4419-7515-7 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2010938895 Mathematics Subject Classicication (2010): Primary: 46Bxx Secondary: 46A03, 46A20, 46A22, 46A25, 46A30, 46A32, 46A50, 46A55, 46B03, 46B04, 46B07, 46B10, 46B15, 46B20, 46B22, 46B25, 46B26, 46B28, 46B45, 46B50, 46B80, 46C05, 46C15, 46G05, 46G12, 47A10, 52A07, 52A21, 52A41, 58C20, 58C25 c Springer Science+Business Media, LLC 2011 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
Many problems in modern linear and nonlinear analysis are of infinite-dimensional nature. The theory of Banach spaces provides a suitable framework for the study of these areas, as it blends classical analysis, geometry, topology, and linearity. This in turn makes Banach space theory a wonderful and active research area in Mathematics. In infinite dimensions, neighborhoods of
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