Subproduct and Product Systems of C* - Algebras

Date
2019-08
Authors
Ketelboeter, Brian
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Faculty of Graduate Studies and Research, University of Regina
Abstract

This thesis initiates the theory of Tsirelson C -subproduct and product systems on a solid basis of results, which extends Arveson's theory of product systems of Hilbert spaces, with emphasis on Tsirelson's two parameter version of product systems of Hilbert spaces. Within we prove that every Tsirelson C -subproduct system admits a Bhat-type dilation to a Tsirelson C -product system, analogous to the Bhat dilation of a conservative quantum dynamical semigorup to an E0-semigroup. We also construct the universal C -algebra of an arbitrary unital Tsirelson C -subproduct system that, together with its associated quantum L evy process, reflect the behavior of the system. Finally, we provide a Arveson-Powers classi cation type scheme of unital Tsirelson C -subproduct and product systems, based on the concept of unit. We also give a description of the units of a spatial Tsirelson C -subproduct system at the level of the state-space of its universal C -algebra, and show that every unit gives rise to an algebraic Tsirelson subproduct system of Hilbert spaces via the GNS construction.

Description
A Thesis Submitted to the Faculty of Graduate Studies and Research In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Mathematics, University of Regina. iv, 70 p.
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