2-Local derivations on AW${}^{\ast }$-algebras of type I

Abstract

It is proved that every 2-local derivation on an AW${}^{\ast }$-algebra of type I is a derivation. Also an analog of Gleason theorem for signed measures on projections of homogenous AW${}^{\ast }$-algebras except the cases of an AW${}^{\ast }$-algebra of type I${}_2$ and a factor of type I${}_m$, $2<m<\infty$ is proved.

arXiv comment17 pages