Weak-2-local ⁎-derivations on B(H)B(H) are linear ⁎-derivations

We prove that, for every separable complex Hilbert space H, every weak-2-local ⁎-derivation on B(H)B(H) is a linear ⁎-derivation. We also establish that every (non-necessarily linear nor continuous) weak-2-local derivation on a finite dimensional C⁎-algebra is a linear derivation.