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

Abstract

Let \(\mathcal{A}\) be a unital Banach algebra such that any Jordan derivation from \(\mathcal{A}\) into any \(\mathcal{A}\)-bimodule \(\mathcal{M}\) is a derivation. We prove that any 2-local derivation from the algebra $M_n(\mathcal{A})$ into $M_n(\mathcal{M})$ $(n\ge 3)$ 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.

12 pages

References in corpus (4)

• $2$-Local derivations on von Neumann algebras
• Local derivations on Rings containing a von Neumann algebra and a question of Kadison
• Local And 2-Local Derivations On Algebras Of Measurable Operators
• Derivations and 2-local derivations on matrix algebras over commutative algebras