Selected Preserver Problems on Algebraic Structures of Linear Operators and on Function Spaces
Over the past several decades, the territory of preserver problems has been continuously enlarging within the frame of linear analysis. The aim of this work is to present a sort of cross-section of the modern theory of preservers on infinite dimensional s
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Lajos Molnár
Selected Preserver Problems on Algebraic Structures of Linear Operators and on Function Spaces
1895
Lecture Notes in Mathematics Editors: J.-M. Morel, Cachan F. Takens, Groningen B. Teissier, Paris
1895
L. Molnár
Selected Preserver Problems on Algebraic Structures of Linear Operators and on Function Spaces
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Author Lajos Molnár Institute of Mathematics University of Debrecen 4010 Debrecen, P.O. Box 12 Hungary e-mail: [email protected]
Library of Congress Control Number: 2006931934 Mathematics Subject Classification (2000): Primary: 47B49, 81R15 ISSN print edition: 0075-8434 ISSN electronic edition: 1617-9692 ISBN-10 3-540-39944-5 Springer Berlin Heidelberg New York ISBN-13 978-3-540-39944-5 Springer Berlin Heidelberg New York DOI 10.1007/3-540-39944-5 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com c Springer-Verlag Berlin Heidelberg 2007 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting by the author and SPi using a Springer LATEX package Cover design: WMXDesign GmbH, Heidelberg Printed on acid-free paper
SPIN: 11857136
VA41/3100/SPi
543210
To my family
Preface
Originally this work served as the author’s dissertation for the scientific title “Doctor of the Hungarian Academy of Sciences”. To publish it in the form of a book has been initiated by the referees who formulated this suggestion in their reports. In what follows we present a cross-section of recent research concerning preserver problems (both linear and non-linear) and local transformations (namely, local automorphisms and local isometries) defined on algebraic structures of linear operators and on function spaces. Generally speaking, preserver problems concern the question of determining or describing the general form of all transformations of a given structure X which preserve • • •
a quantity attached to the elements of X , or a distinguished set of elements of X , or a given relation among the elements of X ,
etc. Such problems arise in most parts of mathematics. In fact, it turns out that in many cases the corresponding results provide important information on the automorphisms of the underlying structures. However, preserver problems are systematically studied only within the scope of matri
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