The Structure of Operator Systems on Finite-Dimensional Hilbert Spaces

Date
2012-04
Authors
Mwangangi, Sadia Hassan
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Faculty of Graduate Studies and Research, University of Regina
Abstract

The purpose of this thesis is to describe in detail the structure of arbitrary operator systems S B(H), where H is assumed to be of finite dimension, using Arveson's non-commutative Choquet theory, and to determine the C* -envelope of S in certain special cases of interest. Arveson classifies these operator systems as either reduced or non-reduced, and we look at these classifications in detail. S is said to be reduced when its boundary ideal is {0} and non-reduced otherwise. We will give examples of 2-dimensional and 3-dimensional operator systems; show what Arveson's parametrization would be in such cases; and determine the C*-envelopes and boundary ideals.

Description
A Thesis Submitted to the Faculty of Graduate Studies and Research In Partial Fulfillment of the Requirements for the Degree of Master of Science degree in Mathematics, University of Regina. v, 65 l.
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