Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Journal of Operator Theory đề tài:Hầu hết thống nhất liên tục automorphism nhóm đại số nhà điều hành. | J. OPERATOR THEORY 8 1982 227-277 Copylight by INCREST 1982 ALMOST UNIFORMLY CONTINUOUS AUTOMORPHISM GROUPS OF OPERATOR ALGEBRAS GEORGE A. ELLIOTT and LÁSZLÓ ZSID0 INTRODUCTION Consider the following property of a C -dynamical system A G a where G is an abelian locally compact group and a is a strongly continuous homomorphism G - 71 a leaves each primitive ideal of A invariant the homomorphism from G into the automorphism group of each primitive quotient of A induced by a has compact spectrum equivalently is uniformly continuous and the covering size of this compact spectrum is bounded by a number which is independent of the primitive quotient. By the covering size of a compact subset of G we mean the smallest number of translates of a fixed compact neighbourhood of 0 in G needed to cover it. Note that any two compact neighbourhoods of 0 in G give essentially the same notions of covering size each bounded by a multiple of the other. In this paper this property of a C -dynamical system together with the analogous property of a IPMynamical system is shown to arise naturally in connection with the following question concerning the case G R. Let X be a complex Banach space endowed with an appropriate weak topology T. and let a be a T-continuous one-parameter group of T-continuous linear isometries on X. In 3 a certain operator associated with a called the analytic generator of a and denoted by a_ is shown to display the following dichotomy cither ơ a_ị G 0 - -oo or ơ a_j c. The case ơ a. c 0 - -oo occurs for example if X is the -space with 1 p 03 associated to a semifinite normal trace on a semifinite -algebra M and a is induced by a weak -continuous one-parameter automorphism group of M 26 Theorem . In 25 it is shown that if X a is a one-parameter c - or W --dy-namical system with X commutative then the case ơ a_j 0 4-oo occurs only if a acts identically. That the case ơ- a_Ị -- c can occur was first pointed out in 23 . 3 . 2324 228 GEORGE A. ELLIOTT and .
