dc.contributor.author Li, Boyu dc.date.accessioned 2018-08-07 13:45:37 (GMT) dc.date.available 2018-08-07 13:45:37 (GMT) dc.date.issued 2018-08-07 dc.date.submitted 2018-07-26 dc.identifier.uri http://hdl.handle.net/10012/13541 dc.description.abstract Dilation theory originated from Sz.Nagy's celebrated dilation theorem which states en that every contractive operator has an isometric dilation. Regular dilation is one of many fruitful directions that aims to generalize Sz.Nagy's dilation theorem to the multi-variate setting. First studied by Brehmer in 1961, regular dilation has since been generalized to many other contexts in recent years. This thesis is a compilation of my recent study of regular dilation on various semigroups. We start from studying regular dilation on lattice ordered semigroups and shows that contractive Nica-covariant representations are regular. Then, we consider the connection between regular dilation on graph products of N, which uni es Brehmer's dilation theorem and the well-known Frazho-Bunce-Popescu's dilation theorem. Finally, we consider regular dilation on right LCM semigroups and study its connection to Nica-covariant dilation. dc.language.iso en en dc.publisher University of Waterloo en dc.subject Nica-covariance en dc.subject Semigroups en dc.subject Dilation en dc.subject Lattice order en dc.title Regular Dilation on Semigroups en dc.type Doctoral Thesis en dc.pending false uws-etd.degree.department Pure Mathematics en uws-etd.degree.discipline Pure Mathematics en uws-etd.degree.grantor University of Waterloo en uws-etd.degree Doctor of Philosophy en uws.contributor.advisor Davidson, Kenneth uws.contributor.affiliation1 Faculty of Mathematics en uws.published.city Waterloo en uws.published.country Canada en uws.published.province Ontario en uws.typeOfResource Text en uws.peerReviewStatus Unreviewed en uws.scholarLevel Graduate en
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