1995/12/20 by William Arveson, Arveson, William
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Geometric and Algebraic Topology #Operator Algebras (math.OA) #funct-an #math.OA
paper · pdf · doi:10.48550/arxiv.funct-an/9512004
13 pages, AMS-TeX, PAM-659
arxiv created 1995/12/20 · openalex publication_date 1995/12/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is known that every semigroup of normal completely positive maps of a von Neumann can be ``dilated" in a particular way to an E0-semigroup acting on a larger von Neumann algebra. The E0-semigroup is not uniquely determined by the completely positive semigroup; however, it is unique (up to conjugacy) provided that certain conditions of \it minimality are met. Minimality is a subtle property, and it is often not obvious if it is satisfied for specific examples even in the simplest case where the von Neumann algebra is \Cal B(H). In this paper we clarify these issues by giving a new characterization of minimality in terms projective cocycles and their limits. Our results are valid for semigroups of endomorphisms acting on arbitrary von Neumann algebras with separable predual.