Unital Dilations of Completely Positive Semigroups: From Combinatorics to Continuity

TL;DR

This paper proves the existence of continuous unital dilations for CP$_0$-semigroups on separable W$^*$-algebras, extending previous ideas and providing a clearer exposition.

Contribution

It introduces a new proof of continuous unital dilations for CP$_0$-semigroups, generalizing prior results and improving understanding of their structure.

Findings

Existence of continuous unital dilations established

Generalizations of Sauvageot's ideas presented

Enhanced exposition of dilation theory provided

Abstract

Using ideas due to Jean-Luc Sauvageot, we prove the existence of a continuous unital dilation of a CP$_0$-semigroup on a separable W$^*$-algebra. This paper presents the material in the author's Ph. D. thesis (arXiv.org:1304.0134.pdf) with some generalizations and an improved exposition.