{"paper":{"title":"Classification of q-pure q-weight maps over finite dimensional Hilbert spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Christopher Jankowski, Daniel Markiewicz, Robert T. Powers","submitted_at":"2018-07-25T18:49:45Z","abstract_excerpt":"An $E_0$-semigroup of $B(H)$ is a one parameter strongly continuous semigroup of $*$-endomorphisms of $B(H)$ that preserve the identity. Every $E_0$-semigroup that possesses a strongly continuous intertwining semigroup of isometries is cocycle conjugate to an $E_0$-semigroup induced by the Bhat induction of a $CP$-flow over a separable Hilbert space $K$. We say an $E_0$-semigroup $\\alpha$ is $q$-pure if the $CP$-subordinates $\\beta$ of norm one (i.e. $\\Vert\\beta_t(I)\\Vert = 1$ and $\\alpha_t-\\beta_t$ is completely positive for all $t \\geq 0$) are totally ordered in the sense that if $\\beta$ and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.09824","kind":"arxiv","version":1},"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"}