Characterizations of *and *-left derivable mappings on some algebras
- Resource Type
- Article
- Authors
- An, Guangyu; He, Jun; Li, Jiankui
- Source
- Annals of Functional Analysis; 20240101, Issue: Preprints p1-13, 13p
- Subject
- Language
- ISSN
- 26397390; 20088752
A linear mapping dfrom a *-algebra Ainto a *-A-bimodule Mis a *-derivable mapping at G?Aif Ad(B)*+d(A)B=d(G)for each A, Bin Awith AB*=G. We prove that every (continuous) *-derivable mapping at Gfrom a (unital C*-algebra) factor von Neumann algebra into its Banach *-bimodule is a *-derivation if and only if Gis a left separating point. A linear mapping dfrom a *-algebra Ainto a *-left A-module Mis a *-left derivable mapping at G?Aif Ad(B)*+Bd(A)=d(G)for each A, Bin Awith 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.