2013/01/11 by Anilesh Mohari, Mohari, Anilesh
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1301.2507
openalex publication_date 2013/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the convex set of ( unital ) positive ( completely ) maps from a C^* algebra \cla to a von-Neumann sub-algebra \clm of \clb(\clh), the algebra of bounded linear operators on a Hilbert space \clh and study its extreme points via its canonical lifting to the convex set of ( unital ) positive ( complete ) normal maps from \cla to \clm, where \cla is the universal enveloping von-Neumann algebra over \cla. If \cla=\clm and a ( complete ) positive operator τ is a unique sum of a normal and a singular ( complete ) positive maps. Furthermore, a unital complete positive map is a unique convex combination of unital normal and singular complete positive maps. We used a duality argument to find a criteria for extremal elements in the convex set of unital completely positive maps having a given faithful normal invariant state. In our investigation, gauge symmetry in Stinespring representation and Kadison theorem on order isomorphism played an important role.