文献类型：期刊文献

英文题名：Characterizations of * and *-left derivable mappings on some algebras

作者：An, Guangyu[1];He, Jun[2];Li, Jiankui[3]

机构：[1]Shaanxi Univ Sci & Technol, Dept Math, Xian 710021, Peoples R China;[2]Anhui Polytech Univ, Dept Math, Wuhu 241000, Peoples R China;[3]East China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China

年份：2020

卷号：11

期号：3

起止页码：680

外文期刊名：ANNALS OF FUNCTIONAL ANALYSIS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000522613000001)】；

基金：The authors thank the referee for his or her suggestions. This research was supported by the National Natural Science Foundation ofChina (Grant Nos. 11801342, 11801005, 11871021); Shaanxi Provincial Education Department (Grant No. 19JK0130).

语种：英文

外文关键词：*-Derivable mapping; *-Left derivable mapping; C *-algebra; Von Neumann algebra

摘要：A linear mapping d from a *-algebra A into a *-A-bimodule M is a *-derivable mapping at G. A if Ad(B)* + d( A) B = d(G) for each A, B in A with AB* = G. We prove that every (continuous) *-derivablemapping at G from a (unital C *-algebra) factor von Neumann algebra into its Banach *-bimodule is a *-derivation if and only if G is a left separating point. A linear mapping d from a *-algebra A into a *-left A-module M is a *-left derivable mapping at G. A if Ad( B)* + Bd( A) = d( G) for each A, B in A with AB* = G. We prove that every continuous *-left derivable mapping at a left separating point from a unital C*-algebra or von Neumann algebra into its Banach *-left A-module is identical with zero under certain conditions.