Dilation theory and som of its applications

Abstract

The purpose of this thesis is to explain some results in dilation theory. In this regard, it has been given the principal results and ideas on positive maps and dilation theory such as Nagy’s theorem, von Neumann’s inequality and some different versions of it, Stinespring’s theorem, dilation for commuting and non-commuting sets of operators, and Shilov boundaries. Also, Nevanlinna-Pick’s interpolation and an application in control theory has been considered.