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 *-σ-derivations, where σis an ultraweakly continuous surjective *-linear mapping. We decompose a $σ$-derivation into a sum of an inner σ-derivation and a multiple of a homomorphism. The so-called *-(σ,τ)-derivations are also discussed.