The Curvature and Index of Completely Positive Maps

2002/07/31 by Paul S. Muhly, Muhly, Paul S., Baruch Solel +1
Mathematics · #46L53 #46L55 #46L57 #46L87 #47L55 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Geometric Analysis and Curvature Flows #Operator Algebras (math.OA) #Quantum Algebra (math.QA) #math.OA #math.QA #msc:46L53 #msc:46L55 #msc:46L57 #msc:46L87 #msc:47L55

paper · pdf · doi:10.48550/arxiv.math/0207298

35 pages, Latex file

arxiv created 2002/07/31 · openalex publication_date 2002/07/31 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study conjugacy invariants for completely positive maps that are inspired by the concept of curvature introduced for commuting d-tuples of contractions by Arveson

Related

• The Curvature of a Single Operator on a Hilbert Space
• The Gromov-Lawson index and the Baum-Connes assembly map
• Note on the Curvature and Index of Almost Unitary Contraction Operator
• Positive scalar curvature and a new index theory for noncompact manifolds
• A relative higher index theorem, diffeomorphisms and positive scalar curvature