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Continuous derivations on \(\ast\)-algebras of \(\tau\)-measurable operators are inner. (English. Russian original) Zbl 1281.46059
Math. Notes 93, No. 5, 654-659 (2013); translation from Mat. Zametki 93, No. 5, 658-664 (2013).
Summary: It is proved that every continuous derivation on the \(\ast\)-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 \(\ast\)-algebra \(S(\mathcal M,\tau)\) is inner. It is proved that every continuous derivation on the \(\ast\)-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 \(\ast\)-algebra \(S(\mathcal M,\tau)\) is inner.

MSC:
46L57 Derivations, dissipations and positive semigroups in \(C^*\)-algebras
46L51 Noncommutative measure and integration
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