Browsing Mathematics (Faculty of) by Subject "operator algebras"
Now showing items 1-6 of 6
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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 ... -
Finitary approximations of free probability, involving combinatorial representation theory
(University of Waterloo, 2023-05-18)This thesis contributes to two theories which approximate free probability by finitary combinatorial structures. The first is finite free probability, which is concerned with expected characteristic polynomials of various ... -
Free semigroup algebras and the structure of an isometric tuple
(University of Waterloo, 2011-06-28)An n-tuple of operators V=(V_1,…,V_n) acting on a Hilbert space H is said to be isometric if the corresponding row operator is an isometry. A free semigroup algebra is the weakly closed algebra generated by an isometric ... -
Maximal ideal space techniques in non-selfadjoint operator algebras
(University of Waterloo, 2013-04-26)The following thesis is divided into two main parts. In the first part we study the problem of characterizing algebras of functions living on analytic varieties. Specifically, we consider the restrictions M_V of the ... -
Representations of Operator Algebras
(University of Waterloo, 2012-05-11)The following thesis is divided into two main chapters. In Chapter 2 we study isometric representations of product systems of correspondences over the semigroup 𝐍ᵏ which are minimal dilations of finite dimensional, fully ... -
Unitary Correlation Sets and their Applications
(University of Waterloo, 2019-07-04)We relate Connes' embedding problem in operator algebras to the Brown algebra Unc(n), which is defined as the universal unital C*-algebra generated by the entries of an n x n unitary matrix. In particular, we show that the ...