Factoriality and Connes' invariant T(M) for free products of von Neumann algebras.
Sums of commutators in ideals and modules of type II factors
Let be a factor of type II or II having separable predual and let be the algebra of affiliated -measurable operators. We characterize the commutator space for sub-- bimodules and of .
The simplex of tracial quantum symmetric states
We show that the space of tracial quantum symmetric states of an arbitrary unital C*-algebra is a Choquet simplex and is a face of the tracial state space of the universal unital C*-algebra free product of A with itself infinitely many times. We also show that the extreme points of this simplex are dense, making it the Poulsen simplex when A is separable and nontrivial. In the course of the proof we characterize the centers of certain tracial amalgamated free product C*-algebras.
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