On a generalized Šemrl’s theorem for weak 2-local derivations on B(H)

Abstract

We prove that, for every complex Hilbert space $H$, every weak 2-local derivation on $B\left(H\right)$ or on $K\left(H\right)$ is a linear derivation. We also establish that every weak 2-local derivation on an atomic von Neumann algebra or on a compact C${}^{\ast }$-algebra is a linear derivation.