$*$-Lie-type maps on $C^*$-algebras

Abstract

Let A and A ′ be two C * -algebras with identities I A and I A ′ , respectively, and P 1 and P 2 = I A − P 1 nontrivial symmetric projections in A . In this paper we study the characterization of multiplicative * -Lie-type maps. In particular, if M is a factor von Neumann algebra then every complex scalar multiplication bijective unital multiplicative * -Lie-type map is * -isomorphism.