Banach Journal of Mathematical Analysis

On generalized ($m, n, l$)-Jordan centralizers of some algebras

Jianbin Guo, Jiankui Li, and Qihua Shen

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Let $\mathcal{A}$ be a unital algebra over a number field $\mathbb{K}$. A linear mapping $\delta$ from $\mathcal{A}$ into itself is called a generalized ($m, n, l$)-Jordan centralizer if it satisfies $(m+n+l)\delta(A^2)-m\delta(A)A-nA\delta(A)-lA\delta(I)A\in \mathbb{K}I$ for every $A\in \mathcal{A}$, where $m\geq0, n\geq0, l\geq0$ are fixed integers with $m+n+l\neq 0$. In this paper, we study generalized ($m, n, l$)-Jordan centralizers on generalized matrix algebras and some reflexive algebras alg$\mathcal{L}$, where $\mathcal{L}$ is a CSL or satisfies $\vee\{L: L\in \mathcal{J}(\mathcal{L})\}=X$ or $\wedge\{L_-: L\in \mathcal{J}(\mathcal{L})\}=(0)$, and prove that each generalized ($m, n, l$)-Jordan centralizer of these algebras is a centralizer when $m+l\geq1$ and $n+l\geq1$.

Article information

Banach J. Math. Anal., Volume 6, Number 2 (2012), 19-37.

First available in Project Euclid: 13 July 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47L35
Secondary: 17B40: Automorphisms, derivations, other operators 17B60: Lie (super)algebras associated with other structures (associative, Jordan, etc.) [See also 16W10, 17C40, 17C50]

CSL algebra centralizer ($m, n, l$)-Jordan centralizer generalized matrix algebra reflexive algebra


Li, Jiankui; Shen, Qihua; Guo, Jianbin. On generalized ($m, n, l$)-Jordan centralizers of some algebras. Banach J. Math. Anal. 6 (2012), no. 2, 19--37. doi:10.15352/bjma/1342210158.

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