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arXiv · 1108.5427

Continuity of derivations in algebras of locally measurable operators

A. F. Ber·V. I. Chilin·F. A. Sukochev
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Abstract

We prove that any derivation of the *-algebra $LS(\mathcal{M})$ of all locally measurable operators affiliated with a properly infinite von Neumann algebra $\mathcal{M}$ is continuous with respect to the local measure topology $t(\mathcal{M})$. Building an extension of a derivation $δ:\mathcal{M}\longrightarrow LS(\mathcal{M})$ up to a derivation from $LS(\mathcal{M})$ into $LS(\mathcal{M})$, it is further established that any derivation from $\mathcal{M}$ into $LS(\mathcal{M})$ is $t(\mathcal{M})$-continuous.

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A. F. Ber, V. I. Chilin, F. A. Sukochev. 2012-06-01. Continuity of derivations in algebras of locally measurable operators. https://arxiv.org/abs/1108.5427

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