Triple derivations on von Neumann algebras

• Autorzy: Robert Pluta , Bernard Russo
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46L57: Derivations, dissipations and positive semigroups in C * -algebras
• 46L10: General theory of von Neumann algebras
• 17C65: Jordan structures on Banach spaces and algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2015
• Tom: 226
• Numer: 1
• Strony: 57-73

Daty

wydano

2015

Twórcy

autor

Robert Pluta

• Department of Mathematics, University of Iowa, Iowa City, IA 52242-1419, U.S.A.

autor

Bernard Russo

• Department of Mathematics, University of California, Irvine, CA 92697-3875, U.S.A.

Identyfikatory

DOI

10.4064/sm226-1-3