Nonlinear maps preserving sums 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 nonlinear maps $\Phi :\mathcal{A}\to \mathcal{B}$ preserving sum of triple products ${\alpha }_{1}abc+{\alpha }_2{a}^{\ast }c{b}^{\ast }+{\alpha }_{3}b{a}^{\ast }c+{\alpha }_{4}ca{b}^{\ast }+{\alpha }_{5}bca+{\alpha }_{6}c{b}^{\ast }{a}^{\ast },$ where the scalars $\{{\alpha }_k{\}}_{k=1}^6$ are complex numbers satisfying some conditions.