Triple derivations on von Neumann algebras
Tom 226 / 2015
Studia Mathematica 226 (2015), 57-73 MSC: Primary 46L57, 17C65; Secondary 46L10. DOI: 10.4064/sm226-1-3
It is well known that every derivation of a von Neumann algebra into itself is an inner derivation and that every derivation of a von Neumann algebra into its predual is inner. It is less well known that every triple derivation (defined below) of a von Neumann algebra into itself is an inner triple derivation.
We examine to what extent all triple derivations of a von Neumann algebra into its predual are inner. This rarely happens but it comes close. We prove a (triple) cohomological characterization of finite factors and a zero-one law for factors.