文献类型：期刊文献

英文题名：Derivations, Local and 2-Local Derivations on Some Algebras of Operators on Hilbert C*-Modules

作者：He, Jun[1];Li, Jiankui[1];Zhao, Danjun[1]

机构：[1]East China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China

年份：2017

卷号：14

期号：6

外文期刊名：MEDITERRANEAN JOURNAL OF MATHEMATICS

收录：;EI(收录号：20200062006);WOS:【SCI-EXPANDED(收录号:WOS:000414103600001)】；

基金：This paper was partially supported by National Natural Science Foundation of China (Grant No. 11371136).

语种：英文

外文关键词：Derivation; Hilbert C*-module; inner derivation; local derivation; 2-local derivation

摘要：For a commutative C*-algebra A with unit e and a Hilbert A-module M, denote by End(A)(M) the algebra of all bounded A-linear mappings on M, and by End*(A)(M) the algebra of all adjointable mappings onM. We prove that ifMis full, then each derivation on End(A)(M) is A-linear, continuous, and inner, and each 2-local derivation on EndA(M) or End*(A)(M) is a derivation. If there exist x(0) in M and f(0) in M', such that f(0)(x(0)) = e, where M' denotes the set of all bounded A-linear mappings fromMto A, then each A-linear local derivation on End(A)(M) is a derivation.