2-Local derivations on matrix algebras over semi-prime Banach algebras and on AW*-algebras

Algebra, Analysis and Quantum Probability

Ayupov, Shavkat^1 ; Kudaybergenov, Karimbergen^2

Dormon Yoli 29, Institute of Mathematics, National University of Uzbekistan, Tashkent

100125, Uzbekistan^1

Ch. Abdirov 1, Department of Mathematics, Karakalpak State University, Nukus

230113, Uzbekistan^2

关键词: Banach algebra;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/697/1/012001/pdf
DOI  :  10.1088/1742-6596/697/1/012001

来源: IOP

【 摘 要 】

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 M 2n(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.