Semi-centralizing maps of generalized matrix algebras
The present article is a continuation of a former work by \textit{Z. Xiao} and \textit{F. Wei} [Linear Algebra Appl. 433, No. 11--12, 2178--2197 (2010; Zbl 1206.15016)]. Motivated by Brešar's and Cheung's ideas, the authors study semi-centralizing maps of generalized matrix algebras and describe its general form by routine and complicated computations. Skew-commuting maps and semi-centralizing maps of generalized matrix algebras are specially considered. They prove that any skew-commuting map on a class of generalized matrix algebras is zero and that any semi-centralizing derivation on a generalized matrix algebra is zero. These results give new perspectives to the work of \textit{M. Brešar} [Taiwanese J. Math. 8, No. 3, 361--397 (2004; Zbl 1078.16032)] and extend the main results of \textit{W.-S. Cheung} [J. Lond. Math. Soc., II. Ser. 63, No. 1, 117--127 (2001; Zbl 1014.16035)]. A number of applications related to semi-centralizing maps are given.
scientific article; zbMATH DE number 6012747
scientific article