{"paper":{"title":"On the existence of $E_{0}$-semigroups -- the multiparameter case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"S.P.Murugan, S.Sundar","submitted_at":"2017-10-12T04:40:47Z","abstract_excerpt":"Let $P \\subset \\mathbb{R}^{d}$ be a closed convex cone. Assume that $P$ is pointed, i.e. the intersection $P \\cap -P=\\{0\\}$ and $P$ is spanning, i.e. $P-P=\\mathbb{R}^{d}$. Denote the interior of $P$ by $\\Omega$. Let $E$ be a product system over $\\Omega$. We show that there exists an infinite dimensional separable Hilbert space $\\mathcal{H}$ and a semigroup $\\alpha:=\\{\\alpha_x\\}_{x \\in P}$ of unital normal $*$-endomorphisms of $B(\\mathcal{H})$ such that $E$ is isomorphic to the product system associated to $\\alpha$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.04649","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1710.04649/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}