文献类型：期刊文献

英文题名：Annihilator-preserving maps, multipliers, and derivations

作者：Li, Jiankui[2];Pan, Zhidong[1]

机构：[1]Saginaw Valley State Univ, Dept Math, University Ctr, MI 48710 USA;[2]E China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China

年份：2010

卷号：432

期号：1

起止页码：5

外文期刊名：LINEAR ALGEBRA AND ITS APPLICATIONS

收录：;EI(收录号：20141517558956);WOS:【SCI-EXPANDED(收录号:WOS:000272954400002)】；

语种：英文

外文关键词：Annihilator; Derivation; Directed graph; Multiplier

摘要：For a commutative subspace lattice L in a von Neumann algebra N and a bounded linear map f : N boolean AND alg L -> B(H), we show that if Af (B)C = 0 for all A, B, C is an element of N boolean AND alg L satisfying AB = BC = 0, then f is a generalized derivation. For a unital C*-algebra A, a unital Banach A-bimodule M, and a bounded linear map f : A -> M, we prove that if f (A) B = 0 for all A, B is an element of A with AB = 0. then f is a left multiplier; as a consequence, every bounded local derivation from a C*-algebra to a Banach A-bimodule is a derivation. We also show that every local derivation on a semisimple free semigroupoid algebra is a derivation and every local multiplier on a free semigroupoid algebra is a multiplier. (C) 2009 Elsevier Inc. All rights reserved.