Dilation theorems for contractive semigroups

TL;DR

This paper presents dilation theorems for contraction semigroups on Hilbert spaces, consolidating known results for reference and further study in operator theory.

Contribution

It compiles and records dilation theorems for contraction semigroups, some of which are known or likely known, from the author's PhD research.

Findings

Dilation theorems for contraction semigroups on Hilbert spaces

Consolidation of known results for reference

Theorems proved during PhD under supervision of Baruch Solel

Abstract

This note records some dilation theorems about contraction semigroups on a Hilbert space - all of which fall into the categories "known" or "probably known" - that I proved while working on my PhD in mathematics (under the supervision of Baruch Solel). It is convenient to have them recorded for reference.