On Jordan centralizers of triangular algebras

Abstract

Let $\mathcal{A}$ be a unital algebra over a number field $\mathbb{F}$. A linear mapping $\varphi$ from $\mathcal{A}$ into itself is called a Jordan-centralized mapping at a given point $G\in \mathcal{A}$ if $\varphi (AB+BA)=\varphi \left(A\right)B+\varphi \left(B\right)A=A\varphi \left(B\right)+B\varphi \left(A\right)$ for all $A$, $B\in \mathcal{A}$ with $AB=G$. In this paper, it is proved that each Jordan-centralized mapping at a given point of triangular algebras is a centralizer. These results are then applied to some non-self-adjoint operator algebras.