{"paper":{"title":"Hilbert $C^*$-module independence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"J. Hamhalter, M. S. Moslehian, R. Eskandari, V. M. Manuilov","submitted_at":"2021-04-19T17:41:03Z","abstract_excerpt":"We introduce the notion of Hilbert $C^*$-module independence: Let $\\mathscr{A}$ be a unital $C^*$-algebra and let $\\mathscr{E}_i\\subseteq \\mathscr{E},\\,\\,i=1, 2$, be ternary subspaces of a Hilbert $\\mathscr{A}$-module $\\mathscr{E}$. Then $\\mathscr{E}_1$ and $\\mathscr{E}_2$ are said to be Hilbert $C^*$-module independent if there are positive constants $m$ and $M$ such that for every state $\\varphi_i$ on $\\langle \\mathscr{E}_i,\\mathscr{E}_i\\rangle,\\,\\,i=1, 2$, there exists a state $\\varphi$ on $\\mathscr{A}$ such that \\begin{align*} m\\varphi_i(|x|)\\leq \\varphi(|x|) \\leq M\\varphi_i(|x|^2)^{\\frac{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.09481","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2104.09481/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"}