On a generalized Semrl'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 $B(H)$ or on $K(H)$ 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.

References in corpus (3)

• $2$-Local derivations on von Neumann algebras
• Local triple derivations on C*-algebras and JB*-triples
• Weak 2-local derivations on ${\mathbb{M}}_n$

Cited by in corpus (2)

• Two-Local derivations on associative and Jordan matrix rings over commutative rings
• Inner derivations and weak-2-local derivations on the C${}^{\ast }$-algebra $C_0(L,A)$