arXiv:math/0510267 Abstract

arXiv:math/0510267 [math.FA]Abstract References Reviews Resources

A Kadison-Sakai Type Theorem

Published 2005-10-13, updated 2008-01-07Version 2

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.

Comments: 10 pages, completely revised

Categories: math.FA, math.OA

Subjects: 46L57, 46L05, 47B47

Keywords: kadison-sakai type theorem, celebrated kadison-sakai theorem states, von neumann algebra, derivation, ultraweakly continuous

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