Elementary Functional Analysis
This text is intended for a one-semester introductory course in functional analysis for graduate students and well-prepared advanced undergraduates in mathematics and related fields. It is also suitable for self-study, and could be used for an independent
- PDF / 1,823,882 Bytes
- 212 Pages / 439.37 x 666.142 pts Page_size
- 98 Downloads / 198 Views
253
Editorial Board
S. Axler K.A. Ribet
Graduate Texts in Mathematics
For other titles published in this series, go to http://www.springer.com/series/136
Barbara D. MacCluer
Elementary Functional Analysis
ABC
Barbara D. MacCluer Department of Mathematics University of Virginia P.O.Box 400137 Charlottesville VA 22904-4137 USA [email protected]
Editorial Board S. Axler
K.A. Ribet
Mathematics Department San Francisco State University San Francisco, CA 94132 USA [email protected]
Mathematics Department University of California, Berkeley Berkeley, CA 94720-3840 USA [email protected]
ISBN: 978-0-387-85528-8 DOI: 10.1007/978-0-387-85529-5
e-ISBN: 978-0-387-85529-5
Library of Congress Control Number: 2008937759 Mathematics Subject Classification ( 2000 ) : 46-01, 47-01 c Springer Science+Business Media, LLC 2009 ° 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.com
To Tom, Josh, and David
Preface Functional analysis arose in the early twentieth century and gradually, conquering one stronghold after another, became a nearly universal mathematical doctrine, not merely a new area of mathematics, but a new mathematical world view. Its appearance was the inevitable consequence of the evolution of all of nineteenth-century mathematics, in particular classical analysis and mathematical physics. Its original basis was formed by Cantor’s theory of sets and linear algebra. Its existence answered the question of how to state general principles of a broadly interpreted analysis in a way suitable for the most diverse situations. A.M. Vershik ([45], p. 438).
This text evolved from the content of a one semester introductory course in functional analysis that I have taught a number of times since 1996 at the University of Virginia. My students have included first and second year graduate students preparing for thesis work in analysis, algebra, or topology, graduate students in various departments in the School of Engineering and Applied Science, and several undergraduate mathematics or physics majors. After a first draft of the manuscript was completed, it was also used for an independent reading course for several undergraduates preparing for graduate school. While this book is short, comparatively speaking, it does not accomplish it aims through brevity. Arguments are generally presented in detail, and in f
Data Loading...
