$\ast$-Jordan-type maps on $C^{\ast }$-algebras

Abstract

Let $\mathfrak{A}$ and ${\mathfrak{A}}^{\prime }$ be two $C^{\ast }$-algebras with identities $I_{\mathfrak{A}}$ and $I_{{\mathfrak{A}}^{\prime }}$, respectively, and $P_1$ and $P_2=I_{\mathfrak{A}}-P_1$ nontrivial projections in $\mathfrak{A}$. In this paper we study the characterization of multiplicative $\ast$-Jordan-type maps. In particular, if $\mathcal{M}$ is a factor von Neumann algebra then every bijective unital multiplicative $\ast$-Jordan-type maps are $\ast$-ring isomorphisms.

14 pages