Mathematics – Operator Algebras
Scientific paper
2007-01-11
Mathematics
Operator Algebras
22 pages. A significant revision, including a new section and many clarifications. No change in the basic mathematics
Scientific paper
Let S be an operator system -- a self-adjoint linear subspace of a unital C*-algebra A such that contains 1 and A=C*(S) is generated by S. A boundary representation for S is an irreducible representation \pi of C*(S) on a Hilbert space with the property that $\pi\restriction_S$ has a unique completely positive extension to C*(S). The set $\partial_S$ of all (unitary equivalence classes of) boundary representations is the noncommutative counterpart of the Choquet boundary of a function system $S\subseteq C(X)$ that separates points of X. It is known that the closure of the Choquet boundary of a function system S is the Silov boundary of X relative to S. The corresponding noncommutative problem of whether every operator system has "sufficiently many" boundary representations was formulated in 1969, but has remained unsolved despite progress on related issues. In particular, it was unknown if $\partial_S$ is nonempty for generic S. In this paper we show that every separable operator system has sufficiently many boundary representations. Our methods use separability in an essential way.
No associations
LandOfFree
The noncommutative Choquet boundary does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The noncommutative Choquet boundary, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The noncommutative Choquet boundary will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-643028