2-Local derivations and automorphisms on $B(H)$
  The paper is devoted to 2-local derivations and 2-local automorphisms on the algebra $B(H)$ of all bounded linear operators on a Hilbert space $H.$ We prove that every 2-local derivation on $B(H)$ is a derivation. A similar result is obtained for automorphisms. 
Sh. A. Ayupov, K. K. Kudaybergenov
math.OA