In this paper, it is shown that if $\mathcal {A}$ is a CSL subalgebra of a von Neumann algebr and $\phi$ is a continuous mapping on $\mathcal {A}$ such that $(m+n+k+l)\phi(A^{2})-(m\phi(A)A+nA\phi(A)+k\phi(I)A^2+l A^2 \phi(I))\in \mathbb{F}I $ for any $A\in \mathcal {A}$, where $\mathbb{F}$ is the real field or the complex field, then $\phi$ is a centralizer. It is also shown that if $\phi$ is an additive mapping on $\mathcal {A}$ such that $(m+n+k+l)\phi(A^{2})=m\phi(A)A+nA\phi(A)+k\phi(I)A^2+l A^2 \phi(I) $for any $A\in\mathcal{A}$, then $\phi$ is a centralizer.
@article{30008,
title = {The characterization of generalized Jordan centralizers on algebras},
journal = {Boletim da Sociedade Paranaense de Matem\'atica},
volume = {35},
year = {2016},
doi = {10.5269/bspm.v35i3.30008},
language = {EN},
url = {http://dml.mathdoc.fr/item/30008}
}
Chen, Quanyuan; Fang, Xiaochun; Li, Changjing. The characterization of generalized Jordan centralizers on algebras. Boletim da Sociedade Paranaense de Matemática, Tome 35 (2016) . doi : 10.5269/bspm.v35i3.30008. http://gdmltest.u-ga.fr/item/30008/