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
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. | en |
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 |