J. Korean Math. Soc. 2017; 54(2): 685-696
Online first article December 27, 2016 Printed March 1, 2017
https://doi.org/10.4134/JKMS.j160265
Copyright © The Korean Mathematical Society.
Jun He, Jiankui Li, and Wenhua Qian
East China University of Science and Technology, East China University of Science and Technology, East China Normal University
A linear mapping $\phi$ on an algebra $\mathcal{A}$ is called a centralizable mapping at $G\in\mathcal{A}$ if $\phi(AB)=\phi(A)B=A\phi(B)$ for each $A$ and $B$ in $\mathcal{A}$ with $AB=G$, and $\phi$ is called a derivable mapping at $G\in\mathcal{A}$ if $\phi(AB)=\phi(A)B+A\phi(B)$ for each $A$ and $B$ in $\mathcal{A}$ with $AB=G$. A point $G$ in $\mathcal{A}$ is called a full-centralizable point (resp. full-derivable point) if every centralizable (resp. derivable) mapping at $G$ is a centralizer (resp. derivation). We prove that every point in a von Neumann algebra or a triangular algebra is a full-centralizable point. We also prove that a point in a von Neumann algebra is a full-derivable point if and only if its central carrier is the unit.
Keywords: centralizer, derivation, full-centralizable point, full-derivable point, von Neumann algebra, triangular algebra
MSC numbers: 47B47, 47L35
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