{"paper":{"title":"Pure inductive limit state and Kolmogorov's property-II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Anilesh Mohari","submitted_at":"2011-01-31T13:38:43Z","abstract_excerpt":"A translation invariant state $\\omega$ on $C^*$-algebra $\\clb=\\otimes_{k \\in \\IZ}M^{(k)}$, where $M^{(k)}=M_d(\\IC)$ 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 $\\tau$ on a von-Neumann algebra $\\clm$ with a faithful normal invariant state $\\phi$. We give an asymptotic criteria on the Markov map $(\\clm,\\tau,\\phi)$ for purity of $\\omega$. Such a pure $\\omega$ gives only type-I or type-III factor $\\omega_R$ once restricted to one side of the chain $\\clb_R=\\otimes_{\\IZ_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.5961","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}