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

2014/09/19 by Shavkat Ayupov, Ayupov, Shavkat, Farkhad Arzikulov +1
Mathematics · #46L51 #46L57 #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:46L51 #msc:46L57

paper · pdf · doi:10.48550/arxiv.1409.5571

17 pages

arxiv created 2015/07/09 · arxiv updated 2015/07/10

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 I₂ and a factor of type I_m, 2<m<∞ is proved.

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