2010/05/24 by Christopher Jankowski, Christopher J. Jankowski, Jankowski, Christopher · 1 citation
Mathematics · #46L07 (Primary) #46L57 (Secondary) #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #math.FA #math.OA #msc:46L07 #msc:46L57
paper · pdf · doi:10.48550/arxiv.1005.4404
30 pages
arxiv created 2010/05/24 · openalex publication_date 2010/05/24 · arxiv updated 2010/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
From previous work, we know how to obtain type II0 E0-semigroups using boundary weight doubles (ϕ, ν), where ϕ: Mn(\C) → Mn(\C) is a unital q-positive map and νis a normalized unbounded boundary weight over L2(0, ∞). In this paper, we classify the unital q-positive maps ϕ: M2(\C) → M2(\C). We find that every unital q-pure map ϕ: M2(\C) → M2(\C) is either rank one or invertible. We also examine the case n=3, finding the limit maps Lϕfor all unital q-positive maps ϕ: M3(\C) → M3(\C). In conclusion, we present a cocycle conjugacy result for E0-semigroups induced by boundary weight doubles (ϕ, ν) when νhas the form ν(√(I - Λ(1)) B √(I - Λ(1)))=(f,Bf).