Vern Paulsen, Department of Pure Mathematics, University of Waterloo
“Embezzlement and states on minimal tensor products”
The minimal tensor product of two C*-algebras is defined spatially, but this does not imply that when we represent it on a Hilbert space that the Hilbert space needs to be a tensor product. A trickier issue is whether or not a given state on a minimal tensor product has a realization as a vector state via a representation of the algebra that is a tensor product representation. This question, as so many things, is related to Connes embedding conjecture.
Embezzlement of states is a construction from mathematical physics that lends some insight into this question.
MC 5417