TAILIEUCHUNG - Báo cáo toán học: "Decomposable operators and automatic continuity "

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Journal of Operator Theory đề tài: Phân huỷ trong các nhà khai thác và liên tục tự động. | s. OPERATOR THEORY 15 1986 33-51 Copyright by INCREST 1986 DECOMPOSABLE OPERATORS AND AUTOMATIC CONTINUITY K. B. LAURSEN and M. M. NEUMANN INTRODUCTION This paper introduces a class of decomposable operators for which it is possible to give a very useful algebraic description of the spectral maximal subspaces. This class the super-decomposable operators is a subset of the strongly decomposable operators. After developing the basic theory we relate this notion to the classical ones and present several wide classes of examples among them multiplication operators. This leads naturally to questions about multipliers in Section 3 an investigation is made of some of the relationships between super-decomposability of a multiplier on a Banach algebra and of the corresponding multiplication operator on the algebra of multipliers. Finally in Section 4 we present some applications to automatic continuity theory. We give necessary and sufficient conditions on a decomposable operator T c E Ỵ and a super-decomposable operator Se K that every linear map 0 X Y for which 0T so be automatically continuous. This generalizes work of Vrbová 23 24 . Among the corollaries of this is the following if 0 LP R - - L R 1 p q oo commutes with some non-trivial transfation operator then 0 is continuous. The authors want to thank Ernst Albrecht and the referee for several helpful comments. The second author was supported in part by the Danish Ministry of Education and by the Deutsche Akademische Austauschdienst. This support is acknowledged with thanks. 1. DECOMPOSABLE OPERATORS AND DIVISIBLE SUBSPACES Throughout this paper we shall use the standard notions and some basic results of the theory of decomposable operators as presented in 12 and 22 Let V C denote the family of all closed subsets of c and let be the space of al 1 3 - 1481 34 K. B. LAURSEX and M. M. continuous linear operators on a complex Banach space X. Given an operator T e 2- X let Lat T stand for the collection of all

• Báo cáo khoa học
• báo cáo của tạp chí Journal of Operator Theory
• tài liệu báo cáo nghiên cứu khoa học
• cách trình bày báo cáo
• kiến thức toán học
• báo cáo toán học
• tài liệu báo cáo nghiện cứu khoa học