*-Jordan-type maps on C^*-algebras

Abstract

Let $\mathfrak{A}$ and $\mathfrak{A}\prime$ be two $C^{*}$-algebras with identities $I_{\mathfrak{A}\mathrm{ }}$ and $I_{\mathfrak{A}\mathrm{ }\prime },$ respectively, and P₁ and $P_2=I_{\mathfrak{A}\mathrm{ }}-P_1$ nontrivial symmetric projections in $\mathfrak{A}$. In this paper we study the characterization of multiplicative $*$-Jordan-type maps. In particular, if $\mathcal{M}$ is a factor von Neumann algebra then every bijective unital multiplicative $*$-Jordan-type maps are $*$-ring isomorphisms.

Keywords:

• C*-algebra
• multiplicative Jordan maps
• multiplicative *-Jordan-type maps

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 17D05
• 46L05