Regular Dilation on Semigroups

Nica-covariance;Semigroups;Dilation;Lattice order

Li, Boyuadvisor:Davidson, Kenneth ; affiliation1:Faculty of Mathematics ; Davidson, Kenneth ;

University of Waterloo

关键词: Lattice order;    Dilation;    Nica-covariance;    Semigroups;    Doctoral Thesis;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/13541/1/Li_Boyu.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

Dilation theory originated from Sz.Nagy's celebrated dilation theorem which statesthat every contractive operator has an isometric dilation. Regular dilation is one of manyfruitful directions that aims to generalize Sz.Nagy's dilation theorem to the multi-variatesetting. First studied by Brehmer in 1961, regular dilation has since been generalized tomany 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 thatcontractive Nica-covariant representations are regular. Then, we consider the connectionbetween regular dilation on graph products of N, which uni es Brehmer's dilation theoremand the well-known Frazho-Bunce-Popescu's dilation theorem. Finally, we consider regulardilation on right LCM semigroups and study its connection to Nica-covariant dilation.