This article is cited in 5 papers

Continuous Derivations on $*$-Algebras of $\tau$-Measurable Operators Are Inner

A. F. Ber

DCF Technologies Ltd.

Abstract: It is proved that every continuous derivation on the $*$-algebra $S(\mathcal{M},\tau)$ of all $\tau$-measurable operators affiliated with a von Neumann algebra $\mathcal{M}$ is inner. For every properly infinite von Neumann algebra $\mathcal{M}$, any derivation on the $*$-algebra $S(\mathcal{M},\tau)$ is inner.

Keywords: von Neumann algebra, properly infinite, $\tau$-measurable operator, continuous derivation.

UDC: 517.98

Received: 14.12.2012

DOI: 10.4213/mzm10231

 English version: Mathematical Notes, 2013, 93:5, 654–659

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