We prove that every 2-local derivation from the algebra $M_n(\mathcal{ A})(n>2)$ into its bimodule $M_n(\mathcal{ M})$ is a derivation, where $\mathcal{ A}$ is a unital Banach algebra and $\mathcal{ M}$ is a unital $\mathcal{ A}$-bimodule such that each Jordan derivation from $\mathcal{ A}$ into $\mathcal{ M}$ is an inner derivation, and that every 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, Jiang-Su algebra and UHF algebras.
Categories: math.OA