Derivations of AW^∗-algebras are inner

Dorte Olesen

Vol. 53 (1974), No. 2, 555–561

DOI: 10.2140/pjm.1974.53.555

Abstract

Using the theory of spectral subspaces associated with a group of isometries of a Banach space it is proved that each derivation of an AW^∗-algebra is inner. This constructive method of proof yields a generator b for the case of a skewadjoint derivation which is seen to be the unique positive generator such that ∥bp∥ = ∥δ|Ap∥ for each central projection p in the AW^∗-algebra A.

Mathematical Subject Classification 2000

Primary: 46L10

Milestones

Received: 3 April 1973

Published: 1 August 1974