a note on commuting mappings

This extended abstract is based on the journal paper [4] published in the international journal of nonlinear analysis and applications. we present the main results with focus on applications to commutant preservers.this paper studies proper linear mappings on generalized matrix algebras. we characterize their general form and establish necessary and sufficient conditions for properness. applications to commuting mappings, lie centralizers, and lie triple centralizers are investigated. our results extend and unify several known characterizations for triangular algebras and nest algebras.