Semi-centralizing maps of generalized matrix algebras

The present article is a continuation of our former work (Xiao and Wei (2010) [35]) to some extent. Motivated by Brešar's and Cheung's wonderful ideas, we will 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. We 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 not only give new perspectives to the work of Brešar (2004) [6] but also extend the main results of Cheung (2001) [13]. A number of applications related to semi-centralizing maps are given.