Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Centralizing mappings on von Neumann algebras

Author: Matej Brešar
Journal: Proc. Amer. Math. Soc. 111 (1991), 501-510
MSC: Primary 46L57; Secondary 16E50, 46L10, 46L40
MathSciNet review: 1028283
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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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Keywords: Centralizing mapping, commuting mapping, derivation, automorphism, $ \alpha $-derivation, von Neumann algebra, prime ring, semiprime ring, Banach algebra
Article copyright: © Copyright 1991 American Mathematical Society