Functional Analysis
The present book is based on lectures given by the author at the University of Tokyo during the past ten years. It is intended as a textbook to be studied by students on their own or to be used in a course on Functional Analysis, i. e. , the general theor
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Editors S. S. Chern J. L. Doob J. Douglas, jr. A. Grothendieck E. Heinz F. Hirzebruch E. Hopf S. Mac Lane W. Magnus M. M. Postnikov W. Schmidt D. S. Scott K. Stein J. Tits B. L. van der Waerden Managing Editors B. Eckmann J. K. Moser
Kosaku Yosida
Functional Analysis
Fifth Edition
Springer-Verlag Berlin Heidelberg New York 1978
Kosaku Yosida 1157-28 Kajiwara, Kamakura, 247/Japan
AMS Subject Classification (1970): 46-XX
ISBN-13: 978-3-642-96441-1 e-ISBN-13: 978-3-642-96439-8 001: 10.1007/978-3-642-96439-8
Library of Congress Cataloging in Publication Data. Yosida, Kiisaku, 1909Functional analysis (Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, Bd. 123). Bibliography: p. 1. Functional analysis, I. Series. QA320.Y6. 1974. 515'.7.74-12123. This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, . re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee be determined by agreement with the publisher.
© by Springer-Verlag Berlin Heidelberg 1965, 1971, 1974, 1978 Softcover reprint of the hardcover 5th edition 1978 214113140-543210
Preface to the First Edition The present book is based on lectures given by the author at the University of Tokyo during the past ten years. It is intended as a textbook to be studied by students on their own or to be used in a course on Functional Analysis, i.e., the general theory of linear operators in function spaces together with salient features of its application to diverse fields of modern and classical analysis. Necessary prerequisites for the reading of this book are summarized, with or without proof, in Chapter 0 under titles: Set Theory, Topological Spaces, Measure Spaces and Linear Spaces. Then, starting with the chapter on Semi-norms, a general theory of Banach and Hilbert spaces is presented in connection with the theory of generalized functions of S. L. SOBOLEV and L. SCHWARTZ. While the book is primarily addressed to graduate students, it is hoped it might prove useful to research mathematicians, both pure and applied. The reader may pass, e.g., from Chapter IX (Analytical Theory of Semi-groups) directly to Chapter XIII (Ergodic Theory and Diffusion Theory) and to Chapter XIV (Integration of the Equation of Evolution). Such materials as "Weak Topologies and Duality in Locally Convex Spaces" and "Nuclear Spaces" are presented in the form of the appendices to Chapter V and Chapter X, respectively. These might be skipped for the first reading by those who are interested rather in the application of linear operators. In the preparation of the present book, the author has received valuable advice and criticism from many friends. Especially, Mrs. K. HILLE has kindly read through the manuscript as well as the galley and page proofs. Wit
