2-Local derivations on matrix algebras over semi-prime Banach algebras and on<i>AW</i>*-algebras
Shavkat AyupovDormon yoli 29, Institute of Mathematics, National University of Uzbekistan, 100125 Tashkent, UzbekistanKarimbergen KudaybergenovCh. Abdirov 1, Department of Mathematics, Karakalpak state university, Nukus 230113, Uzbekistan
ABI
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 A with the inner derivation property we prove that any 2-local derivation on the algebra M2n (A), n ≥ 2, is a derivation. We apply this result to AW*-algebras and show that any 2-local derivation on an arbitrary AW*-algebra is a derivation.