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Techniques in operator algebras: classification, dilation and non-commutative boundary theory
(University of Waterloo, 2017-08-11)
In this thesis we bring together several techniques in the theory of non-self-adjoint operator algebras and operator systems. We begin with classification of non-self-adjoint and self-adjoint operator algebras constructed ...
Semicrossed Products, Dilations, and Jacobson Radicals
(University of Waterloo, 2017-08-18)
We compute the C*-envelope of the isometric semicrossed product of a C*-algebra arising from number theory by the multiplicative semigroup of a number ring R, and prove that it is isomorphic to T[R], the left regular ...
Regular Dilation on Semigroups
(University of Waterloo, 2018-08-07)
Dilation theory originated from Sz.Nagy's celebrated dilation theorem which states that every contractive operator has an isometric dilation. Regular dilation is one of many fruitful directions that aims to generalize ...
Nevanlinna-Pick Spaces and Dilations
(University of Waterloo, 2016-07-12)
The majority of this thesis is devoted to the study of Nevanlinna-Pick spaces and their multiplier algebras. These spaces are Hilbert function spaces in which a version of the Nevanlinna-Pick interpolation theorem from ...