2-Local derivations on matrix algebras over semi-prime Banach algebras and on $AW^\ast$-algebras

arXiv1411.2472MaRDI QIDQ6256270

Sh. A. Ayupov, Karimbergen Kudaybergenov

Publication date: 10 November 2014

Abstract: The paper is devoted to 2-local derivations on matrix algebras over unital semi-prime Banach algebras. For a unital semi-prime Banach algebra $mathcalA$ with the inner derivation property we prove that any 2-local derivation on the algebra $M_{2^n}(mathcalA),$ $ngeq2,$ is a derivation. We apply this result to $A{W}^{a}st$-algebras and show that any 2-local derivation on an arbitrary $A{W}^{a}st$-algebra is a derivation.

Mathematics Subject Classification ID

Commutators, derivations, elementary operators, etc. (47B47) Derivations, dissipations and positive semigroups in (C^*)-algebras (46L57) Linear operators in (C^*)- or von Neumann algebras (47C15)

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