k-commuting mappings of generalized matrix algebras

In this paper we will study k-commuting mappings of generalized matrix algebras. The general form of arbitrary k-commuting mapping of a generalized matrix algebra is determined. It is shown that under mild assumptions, every k-commuting mapping of a generalized matrix algebra takes a certain form which is said to be proper. A number of applications related to k-commuting mappings are presented. These results extend the existing works of Cheung (J Lond Math Soc 63:117–127, 2001), Du and Wang (Linear Algebra Appl 436:1367–1375 2012) to the case of generalized matrix algebras.