CHARACTERIZATIONS OF CENTRALIZERS AND DERIVATIONS ON SOME ALGEBRAS

• Published in: Journal of the Korean Mathematical Society Vol. 54; no. 2; pp. 685 - 696
• Main Authors: He, Jun, Li, Jiankui, Qian, Wenhua
• Format: Journal Article
• Language: English
• Published: 대한수학회 01.03.2017
• Subjects: 수학
• ISSN: 0304-9914; 2234-3008
• DOI: 10.4134/JKMS.j160265

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. KCI Citation Count: 4