Online Archive of University of Virginia Scholarship
Boundaries for Operator Systems1156 views
Author
Kleski, Craig Matthew, Department of Mathematics, University of Virginia
Advisors
Sherman, David, Department of Mathematics, University of Virginia
Kriete, Thomas, Department of Mathematics, University of Virginia
Rovnyak, James, Department of Mathematics, University of Virginia
Maccluer, Barbara, Department of Mathematics, University of Virginia
Abstract
Let H be a complex Hilbert space, B(H) the bounded linear operators on H, and S a unital, linear subspace of B(H). The set S is an operator system. We investigate boundaries, or norm-attaining sets, for operator systems. In particular, we show that Arveson's noncommutative Choquet boundary for a separable system forms a boundary. We obtain a new characterization of unital completely positive maps having the unique extension property. We show the relationship between various sorts of extreme points of noncommutative convex sets, relate them to boundary representations for operator systems, and prove that operator systems in matrix algebras have a minimal boundary. Finally, we explore noncommutative peaking phenomena for operator systems, proving a partial generalization of the Bishop-de Leeuw theorem for uniform algebras.
Note: Abstract extracted from PDF text
Degree
PHD (Doctor of Philosophy)
Language
English
Rights
All rights reserved (no additional license for public reuse)
Kleski, Craig Matthew. Boundaries for Operator Systems. University of Virginia, Department of Mathematics, PHD (Doctor of Philosophy), 2013-05-01, https://doi.org/10.18130/V34R6D.
