Centralizing mappings on von Neumann algebras

Brešar, Matej

doi:10.1090/S0002-9939-1991-1028283-2

Centralizing mappings on von Neumann algebras
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Proc. Amer. Math. Soc. 111 (1991), 501-510 Request permission

Abstract:

Let $R$ be a ring with center $Z(R)$. A mapping $F$ of $R$ into itself is called centralizing if $F(x)x - xF(x) \in Z(R)$ for all $x \in R$. The main result of this paper states that every additive centralizing mapping $F$ on a von Neumann algebra $R$ is of the form $F(x) = cx + \zeta (x),x \in R$, where $c \in Z(R)$ and $\zeta$ is an additive mapping from $R$ into $Z(R)$. We also consider $\alpha$-derivations and some related mappings, which are centralizing on rings and Banach algebras

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