A Kadison-Sakai Type Theorem

Details A Kadison-Sakai Type Theorem A Kadison-Sakai Type Theorem

2005-10-13

arxiv.org/abs/math/0510267v2

Mathematics

Functional Analysis

10 pages, completely revised

Scientific paper

The celebrated Kadison--Sakai theorem states that every derivation on a von Neumann algebra is inner. In this paper, we prove this theorem for ultraweakly continuous *-\sigma-derivations, where \sigma is an ultraweakly continuous surjective *-linear mapping. We decompose a $\sigma$-derivation into a sum of an inner \sigma-derivation and a multiple of a homomorphism. The so-called *-(\sigma,\tau)-derivations are also discussed.

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