The Structure of Operator Systems on Finite-Dimensional Hilbert Spaces

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dc.contributor.advisor Argerami, Martin Mwangangi, Sadia Hassan 2012-08-31T16:38:02Z 2012-08-31T16:38:02Z 2012-04
dc.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. en_US
dc.description.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. en_US
dc.language.iso en en_US
dc.publisher Faculty of Graduate Studies and Research, University of Regina en_US
dc.subject.lcsh Hilbert space
dc.subject.lcsh Dimensional analysis
dc.subject.lcsh Choquet theory
dc.title The Structure of Operator Systems on Finite-Dimensional Hilbert Spaces en_US
dc.type Thesis en
dc.description.authorstatus Student en
dc.description.peerreview yes en Master of Science (MSc) en_US Master's en Mathematics en_US University of Regina en Department of Mathematics and Statistics en_US
dc.contributor.committeemember Farenick, Douglas
dc.contributor.committeemember Floricel, Remus
dc.contributor.externalexaminer Mobed, Nader
dc.identifier.tcnumber TC-SRU-3561

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