2011/01/31 by Anilesh Mohari, Mohari, Anilesh
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA) #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.1101.5961
openalex publication_date 2011/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A translation invariant state ω on C^*-algebra \clb=⊗k ∈ \IZM(k), where M(k)=Md(\IC) is the d-dimensional matrices over field of complex numbers, give rises a stationary quantum Markov chain and associates canonically a unital completely positive normal map τ on a von-Neumann algebra \clm with a faithful normal invariant state ϕ. We give an asymptotic criteria on the Markov map (\clm,τ,ϕ) for purity of ω. Such a pure ω gives only type-I or type-III factor ωR once restricted to one side of the chain \clbR=⊗\IZ+M(k). In case ωR is type-I, ω admits Kolmogorov's property.