On Real Aw*-Algebras with Abelian Skew-Hermitian Part

Abstract

It is known that, unlike to the complex case, in real * C - algebras R their Hermitian part Rs and skew-hermitian part Rk are not connected by the relation R iR k s = . In [1] described up to * - isomorphism all real * W -algebras with abekian Hermitian part. In paper this result is generalized for the real * AW -algebras. Exactly, it is described up to * -isomorphism all real * AW -algebras with abelian Hermitian part.