Mappings preserving sum of triple products on $\ast$-algebras

Abstract

Let $\mathcal{A}$ and $\mathcal{B}$ be two unital complex $\ast$-algebras such that $\mathcal{A}$ has a nontrivial projection. In this paper, we study the structure of bijective mappings $\Phi :\mathcal{A}\to \mathcal{B}$ preserving sum of triple products ${\alpha }_{1}a{b}^{\ast }c+{\alpha }_{2}ac{b}^{\ast }+{\alpha }_3{b}^{\ast }ac+{\alpha }_{4}ca{b}^{\ast }+{\alpha }_5{b}^{\ast }ca+{\alpha }_{6}c{b}^{\ast }a,$ where the scalars $\{{\alpha }_k{\}}_{k=1}^6$ are complex numbers satisfying some conditions. Applications of obtained results are given.