Unital Dilations of Completely Positive Semigroups: From Combinatorics to Continuity

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${}^{\ast }$-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.

69 pages. Submitted to Memoirs of the AMS

References in corpus (1)

• Continuity of CP-semigroups in the point-strong operator topology

Cited by in corpus (1)

• The Extension of Unital Completely Positive Semigroups on Operator Systems to Semigroups on $C^{\ast }$-algebras