Innerness of continuous derivations on algebras of measurable operators affiliated with finite von Neumann algebras

Abstract

This paper is devoted to derivations on the algebra $S(M)$ of all measurable operators affiliated with a finite von Neumann algebra $M.$ We prove that if $M$ is a finite von Neumann algebra with a faithful normal semi-finite trace $\tau$, equipped with the locally measure topology $t,$ then every $t$-continuous derivation $D:S(M)\to S(M)$ is inner. A similar result is valid for derivation on the algebra $S(M,\tau )$ of $\tau$-measurable operators equipped with the measure topology $t_{\tau }$.

Accepted for publication in the Journal of Mathematical Analysis and Applications

References in corpus (3)

• Derivations in algebras of operator-valued functions
• Additive derivations on algebras of measurable operators
• Continuity of derivations in algebras of locally measurable operators

Cited by in corpus (4)

• Spatiality of derivations on the algebra of $\tau$-compact operators
• Notes on derivations of Murray--von Neumann algebras
• Local derivations on measurable operators and commutativity
• Local derivations on subalgebras of $\tau$-measurable operators with respect to semi-finite von Neumann algebras