Linear Topological Spaces
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Editorial Board: F. W. Gehring P. R. Halmos (Managing Editor) C. C. Moore
Linear Topological Spaces lohn L. Kelley Isaac Namioka and
W. F. Donoghue, Jr. G. Baley Price Kenneth R. Lucas Wendy Robertson B. J. Pettis W. R. Scott Ebbe Thue Poulsen Kennan T. Smith
Springer-Verlag Berlin Heidelberg GmbH
J ohn L. Kelley
Isaac Namioka
Department of Mathematics University of California Berkeley, California 94720
Department of Mathematics University of Washington Seattle, Washington 98195
Editorial Board P. R. Halmos Indiana University Department of Mathematics Swain Hali East Bloomington, Indiana 47401
F. W. Gehring
C. C. Moore
University of Michigan Department of Mathematics Ann Arbor, Michigan 48104
University of California at Berkeley Department of Mathematics Berkeley, California 94720
AMS Subject Classifications
46AXX Library of Congress Cataloging in Publication Data Kelley, John L. Linear topologica! spaces. (Graduate texts in mathematics; 36) Reprint of the ed. published by Van Nostrand, Princeton, N.J., in series: The University series in higher mathematics. Bibliography: p. lncludes index. 1. Linear topological spaces. I. Namioka, Isaac, joint author. IT. Title. ITI. Series. QA322.K44 1976 514'.3 75-41498 Second corrected printing
AII rights reserved. No part of this book may be translated or reproduced in any form without written permission from Springer-Verlag Berlin Heidelberg GmbH 1963 by J. L. Kelley and G. B. Price. Originally published by Springer-Verlag New York Heidelberg Berlin in 1963
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Softcover reprint of the hardcover 1st edition 1963 Originally published in the University Series in Higher Mathematics (D. Van Nostrand Company); edited by M. H. Stone, L. Nirenberg and S. S. Chem. ISBN 978-3-662-41768-3 DOI 10.1007/978-3-662-41914-4
ISBN 978-3-662-41914-4 (eBook)
FOREWORD
THIS BOOK ISA STUDY OF LINEAR TOPOLOGICAL SPACES.
EXPLICITLY, WE
are concerned with a linear space endowed with a topology such that scalar multiplication and addition are continuous, and we seek invariants relative to the dass of all topological isomorphisms. Thus, from our point of view, it is incidental that the evaluation map of a normed linear space into its second adjoint space is an isometry; it is pertinent that this map is relatively open. W e study the geometry of a linear topological space for its own sake, and not as an incidental to the study of mathematical objects which are endowed with a more elaborate structure. This is not because the relation of this theory to other notions is of no importance. On the contrary, any discipline worthy of study must illuminate neighboring areas, and motivation for the study of a new concept may, in great part, lie in the clarification and simplification of more familiar notions. As it turns out, the theory of linear topological spaces provides a remarkable economy in discussion of many classical mathematical problems, so that this theory may properly be considered to be both a synthesis and an extension of older ideas.* The textbegins with an investigation of l
