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Faculty of Graduate Studies and Research, University of Regina
The Structure of Operator Systems on Finite-Dimensional Hilbert Spaces
Abstract
dc:description.abstractThe 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.
Degree
thesis:*- Name thesis:degree_name
- Master of Science (MSc)
- Level thesis:degree_level
- Master's
- Discipline thesis:degree_discipline
- Mathematics
- Grantor dc:publisher
- Faculty of Graduate Studies and Research, University of Regina
- Year dc:date.issued
- 2012
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Mwangangi, Sadia Hassan
- Advisor dc:contributor.advisor
-
- Argerami, Martin
- Committee members dc:contributor.committeemember
-
- Farenick, Douglas
- Floricel, Remus
Rights
- Language dc:language.iso
- en
Identifiers
dc:identifier.*- OAI identifier oai:identifier
- oai:uregina.scholaris.ca:10294/3561