2-Local derivations on matrix algebras and algebras of measurable operators

2017/02/24 by Ayupov, Shavkat, Kudaybergenov, Karimbergen, Alauadinov, Amir
#16W25 #47B47 #FOS: Mathematics #Operator Algebras (math.OA) #Primary 46L57 #Secondary 47C15

paper · doi:10.48550/arxiv.1702.07629

Abstract

Let \(A\) be a unital Banach algebra such that any Jordan derivation from \(A\) into any \(A\)-bimodule \(M\) is a derivation. We prove that any 2-local derivation from the algebra M_n(A) into M_n(M) (n≥ 3) is a derivation. We apply this result to show that any 2-local derivation on the algebra of locally measurable operators affiliated with a von Neumann algebra without direct abelian summands is a derivation.

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