Commutator representations of covariant differential calculi
Let be an inclusion of factors with finite Jones index. Then as a vector space. Here denotes the vector space spanned by the commutators of the form where .
We consider compactness, weak compactness and complete continuity for multiplication operators on von Neumann algebras and their preduals.
Last years, the search for a good theory of quantum dynamical entropy has been very much intensified. This is not only due to its usefulness in quantum probability but mainly because it is a very promising tool for the theory of quantum chaos. Nowadays, there are several constructions which try to fulfill this need, some of which are more mathematically inspired such as CNT (Connes, Narnhofer, Thirring), and the one proposed by Voiculescu, others are more inspired by physics such as ALF (Alicki,...
We describe the subspaces of (1 ≤ p ≠ 2 < ∞) which are the range of a completely contractive projection.
In this paper, we introduce and study the notion of completely bounded sets ( for short) for compact, non-abelian groups G. We characterize sets in terms of completely bounded multipliers. We prove that when G is an infinite product of special unitary groups of arbitrarily large dimension, there are sets consisting of representations of unbounded degree that are sets for all p < ∞, but are not for any p ≥ 4. This is done by showing that the space of completely bounded multipliers...
A KSGNS (Kasparov, Stinespring, Gel'fand, Naimark, Segal) type construction for strict (respectively, covariant non-degenerate) completely multi-positive linear maps between locally C*-algebras is described.