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2-Local derivations on AW$^*$-algebras of type I

Published 19 Sep 2014 in math.OA | (1409.5571v2)

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

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