The monograph is devoted to a systematic study of means of Hilbert space operators by a unified method based on the theory of double integral transformations and Peller's characterization of Schur multipliers. General properties on means of operators such as comparison results, norm estimates and convergence criteria are established. After some general theory, special investigations are focused on three one-parameter families of A-L-G (arithmetic-logarithmic-geometric) interpolation means, Heinz-type means and binomial means. In particular, norm continuity in the parameter is examined for such means. Some necessary technical results are collected as appendices.
Lecture Notes in Mathematics Editors: J.--M. Morel, Cachan F. Takens, Groningen B. Teissier, Paris 1820 3 Berlin Heidelberg New York Hong Kong London Milan Paris Tokyo Fumio Hiai Hideki Kosaki Means of Hilbert Space Operators 13 Authors Fumio Hiai Graduate School of Information Sciences Tohoku University Aoba-ku, Sendai 980-8579 Japan e-mail:
[email protected] Hideki Kosaki Graduate School of Mathematics Kyushu University Higashi-ku, Fukuoka 812-8581 Japan e-mail:
[email protected] Cataloging-in-Publication Data applied for Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at http://dnb.ddb.de Mathematics Subject Classification (2000): 47A30, 47A64, 15A60 ISSN 0075-8434 ISBN 3-540-40680-8 Springer