Perturbations of Banach Algebras
- PDF / 5,518,007 Bytes
- 123 Pages / 468 x 684 pts Page_size
- 15 Downloads / 232 Views
1120 Krzysztof Jarosz
Perturbations of Banach Algebras
Springer-Verlag Berlin Heidelberg New York Tokyo
Author Krzysztof Jarosz Institute of Mathematics, Warsaw University P.K.i.N. 9p., 00-901 Warsaw, Poland
AMS Subject Classification (1980): Primary: 46J05, 46J 10, 46B20; secondary: 46-02, 46E25, 46H05 ISBN 3-540-15218-0 Springer-Verlag Berlin Heidelberg New York Tokyo ISBN 0-387-15218-0 Springer-Verlag New York Heidelberg Berlin Tokyo This work is subject to copyright. All rights are reserved, whether the whole or part of the matenal 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 "Verwertungsgesellschaft Wort", Munich.
© by Springer-Verlag Berlin Heidelberg 1985 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2146/3140-543210
Preface
This work is an introduction to a theory, in its initial stages; its development during the past few years may be seen in the works of Richard Rochberg, Barry E. Johnson as well as those of the author. We investigate various classes of small perturbations of algebraic structure of Banach algebras. We work with small isomorphisms between Banach algebras, with perturbations of multiplication as well as with other kinds of perturbations. In this paper we study the relations occuring between various types of perturbations and certain invariants of perturbations. Much of the material presented here grew out of the author's conversations with Prof. Z. Sawon. I am greatly indebted to him. Many thanks are also due to my wife Dorota for her careful reading of the manuscript.
Warsaw, January 1985 Krzysztof Jarosz
Table of
contents
PRELUUNARIES § 1. Introduction
I. PERTURBATIONS OF MULTIPLICATIONS AND ONTO-ISOMORPHISMS § 2. Basic facts ••••••••••••••••••••••••••••••••••••••••••
4
§ 3. The main theorem •••••.•••••••••••••••••••••••••••••.•
7
§ 4. Proof of the main theorem ••••••••••••••••••••••••••••
17
II. INTO-ISOMORPHISMS § 5. Definitions and examples •••••••••••••••••••••••••••••
36
§ 6. €-embeddings and €-isomorphisms ••••••••••••••••••••••
38
III. ISOMETRIES IN SEMISIMPLE, COMMUTATIVE BANACH ALGEBRAS § 7. Introduction •••••••••••••••••••.•.•••••••••••••••••••
45
§ 8. Definitions and notation •••••••••••••••••••••••••••.•
46
§ 9. Isometries between natural algebras ••••••••••••••••••
47
§10. Small isomorphisms between natural algebras ••••••••••
53
IV. PERTURBATIONS OF OPERATOR ALGEBRAS § 11. Introduction •••••••••••••••••••••••••••••••••••••••••
56
§12. Isometries in operator algebras ••••••••••••••••••••••
57
§13. Small isomorphisms in operator algebras ••••••••••••••
65
V. STABILITY
§14. Introduction
77
§15.
space ••••••••••••••••••••••••••••••••••••••••••••
78
§16. The decomposition of a deformation into antisymmetric algebras •••••••••••••••••••••••••••••••••••••••••••••
Data Loading...
