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Continuity of derivations of algebras of locally measurable operators
Authors:A F Ber  V I Chilin  F A Sukochev
Institution:1. Department of Mathematics, National University of Uzbekistan, Vuzgorodok, 100174, Tashkent, Uzbekistan
2. School of Mathematics and Statistics, University of New South Wales, Sydney, NSW, 2052, Australia
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 ${\delta:{\mathcal{M}}\rightarrow LS({\mathcal{M}})}$ 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.
Keywords:
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