Abstract:

In this paper, we first give the general forms of skew commuting maps and skew anti-commuting maps by the Peirce decomposition on a unital ring with a nontrivial idempotent, respectively, and then, as applications, we obtain the concrete characterizations of all nonadditive skew (anti-)commuting maps on some operator algebras.

Key words: Commuting map, Skew commuting map, Anti-commuting map, Operator algebra