Quasi-linear functionals determined by weak-2-local ${}^{\ast }$-derivations on $B(H)$

Abstract

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