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

preprint2015arXivOpen access

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

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