Browsing Pure Mathematics by Supervisor "Kennedy, Matthew"
Now showing items 1-7 of 7
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Applications of Operator Systems in Dynamics, Correlation Sets, and Quantum Graphs
(University of Waterloo, 2020-07-24)The recent works of Kalantar-Kennedy, Katsoulis-Ramsey, Ozawa, and Dykema-Paulsen have demonstrated that many problems in the theory of operator algebras and quantum information can be approached by looking at various ... -
Classification of Finitely Generated Operator Systems
(University of Waterloo, 2018-01-22)For the past few decades operator systems and their C*-envelopes have provided an invaluable tool for studying the theory of C*-algebras and positive maps. They provide the natural context in which to study the theory of ... -
Coefficient spaces arising from locally compact groups
(University of Waterloo, 2020-08-17)This thesis studies two disjoint topics involving coefficient spaces and algebras associated to locally compact groups. First, Chapter 3 investigates the connection between amenability and compactness conditions on locally ... -
Dilation methods in semigroup dynamics and noncommutative convexity
(University of Waterloo, 2022-08-25)Since seminal work of Stinespring, Arveson, and others, dilation theory has been an indispensable tool for understanding operator algebras. Dilations are fundamental to the representation theory of operator systems and ... -
Exactness and Noncommutative Convexity
(University of Waterloo, 2022-09-02)This thesis studies two separate topics in connection to operator systems theory: the dynamics of locally compact groups, and noncommutative convex geometry. In Chapter 1 we study exactness of locally compact groups as ... -
Graph C*-algebras and the Abelian Core
(University of Waterloo, 2016-08-26)We may associate to a C*-algebra to the directed graph E by associating edges to partial isometries and vertices to pairwise orthogonal Hilbert spaces which satisfy some additional conditions. Such graph algebras were first ... -
Tracial and ideal structure of crossed products and related constructions
(University of Waterloo, 2022-08-17)In this thesis, we concern ourselves with asking questions about the basic structure of group C*-algebras, crossed products, and groupoid C*-algebras. Specifically, we are concerned with two main topics. One is the simplicity ...