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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm226-1-3,
author = {Robert Pluta and Bernard Russo},
title = {Triple derivations on von Neumann algebras},
journal = {Studia Mathematica},
volume = {231},
year = {2015},
pages = {57-73},
zbl = {1338.46078},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm226-1-3}
}
Robert Pluta; Bernard Russo. Triple derivations on von Neumann algebras. Studia Mathematica, Tome 231 (2015) pp. 57-73. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm226-1-3/