$2$-Local derivations on von Neumann algebras

Abstract

The paper is devoted to the description of $2$-local derivations on von Neumann algebras. Earlier it was proved that every $2$-local derivation on a semi-finite von Neumann algebra is a derivation. In this paper, using the analogue of Gleason Theorem for signed measures, we extend this result to type $III$ von Neumann algebras. This implies that on arbitrary von Neumann algebra each $2$-local derivation is a derivation.

7 pages

References in corpus (2)

• 2-local derivations on semi-finite von Neumann algebras
• 2-Local derivations and automorphisms on $B(H)$

Cited by in corpus (8)

• On a generalized Semrl's theorem for weak-2-local derivations on B(H)
• Two-Local derivations on associative and Jordan matrix rings over commutative rings
• Boundedness of completely additive measures with application to 2-local triple derivations
• Characterizations of 2-local derivations and local Lie derivations on some algebras
• 2-local standard isometries on vector-valued Lipschitz function spaces
• Derivations, local and 2-local derivations on some algebras of operators on Hilbert C*-modules
• Inner derivations and weak-2-local derivations on the C${}^{\ast }$-algebra $C_0(L,A)$
• 2-Local derivations on matrix algebras and algebras of measurable operators