A Kadison-Sakai Type Theorem

Abstract

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.