## Banach Journal of Mathematical Analysis

### On Jordan centralizers of triangular algebras

Lei Liu

#### Abstract

Let $\mathcal{A}$ be a unital algebra over a number field $\mathbb{F}$. A linear mapping $\phi$ from $\mathcal{A}$ into itself is called a Jordan-centralized mapping at a given point $G\in\mathcal{A}$ if $\phi(AB+BA)=\phi(A)B+\phi(B)A=A\phi(B)+B\phi(A)$ 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.

#### Article information

Source
Banach J. Math. Anal., Volume 10, Number 2 (2016), 223-234.

Dates
Accepted: 26 May 2015
First available in Project Euclid: 23 February 2016

https://projecteuclid.org/euclid.bjma/1456246277

Digital Object Identifier
doi:10.1215/17358787-3492545

Mathematical Reviews number (MathSciNet)
MR3465811

Zentralblatt MATH identifier
1338.47039

#### Citation

Liu, Lei. On Jordan centralizers of triangular algebras. Banach J. Math. Anal. 10 (2016), no. 2, 223--234. doi:10.1215/17358787-3492545. https://projecteuclid.org/euclid.bjma/1456246277

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