Continuous derivations on algebras of locally measurable operators are inner
A. F. BerDepartment of Mathematics; National University of Uzbekistan; Vuzgorodok 100174 Tashkent UzbekistanV. I. ChilinDepartment of Mathematics; National University of Uzbekistan; Vuzgorodok 100174 Tashkent UzbekistanF. A. SukochevSchool of Mathematics and Statistics; University of New South Wales; Kensington New South Wales 2052 Australia
ABI
Abstract
We prove that every derivation acting on the *-algebra L S ( M ) of all locally measurable operators affiliated with a von Neumann algebra M is necessarily inner provided that it is continuous with respect to the local measure topology. In particular, every derivation on L S ( M ) is inner provided that M is a properly infinite von Neumann algebra. Furthermore, any derivation on an arbitrary von Neumann algebra M with values in a Banach M-bimodule of locally measurable operators is inner.
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