Item Details

Boundaries for Operator Systems

Kleski, Craig Matthew
Format
Thesis/Dissertation; Online
Author
Kleski, Craig Matthew
Advisor
Kriete, Thomas
Sherman, David
Rovnyak, James
Maccluer, Barbara
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
Language
English
Date Received
20140123
Published
University of Virginia, Department of Mathematics, PHD (Doctor of Philosophy), 2013
Published Date
2013-05-01
Degree
PHD (Doctor of Philosophy)
Collection
Libra ETD Repository
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