Indexed by:期刊论文
Date of Publication:2021-01-10
Journal:ADVANCES IN MATHEMATICS
Volume:375
Page Number:107347-
ISSN No.:0001-8708
Key Words:Weyl-von Neumann theorem; Voiculescu's Theorem; Normed ideal; Phi-well-behaved sets; von Neumann algebras
Abstract:In this paper, we provide a generalized version of Voiculescu's theorem for normal operators by showing that, in a von Neumann algebra with separable pre-dual and a faithful, normal, semifinite, tracial weight tau, each normal operator is an arbitrarily small (max{parallel to.parallel to, parallel to.parallel to(2)})-norm perturbation of a diagonal operator. Furthermore, in a countably decomposable, properly infinite von Neumann algebra with a faithful normal semifinite tracial weight, we prove that each self-adjoint operator can be diagonalized modulo normed ideals satisfying a natural condition. An analogue, for nuclear C*-algebras, of Voiculescu's absorption theorem [33, Theorem 2.4] is also proved in the case of semifinite factors. (C) 2020 Elsevier Inc. All rights reserved.