Characterization of 2-Local Derivations and Local Lie Derivations on Some Algebras

Abstract

We prove that each 2-local derivation from the algebra Mn(A ) (n > 2) into its bimodule Mn(M) is a derivation, where A is a unital Banach algebra and M is a unital A -bimodule such that each Jordan derivation from A into M is an inner derivation, and that each 2-local derivation on a C*-algebra with a faithful traceable representation is a derivation. We also characterize local and 2-local Lie derivations on some algebras such as von Neumann algebras, nest algebras, the Jiang–Su algebra, and UHF algebras.