{"paper":{"title":"Unique Pseudo-Expectations for Hereditarily Essential $C^*$-Inclusions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Vrej Zarikian","submitted_at":"2024-06-27T18:57:43Z","abstract_excerpt":"The $C^*$-inclusion $\\mathcal{A} \\subseteq \\mathcal{B}$ is said to be hereditarily essential if for every intermediate $C^*$-algebra $\\mathcal{A} \\subseteq \\mathcal{C} \\subseteq \\mathcal{B}$ and every non-zero ideal $\\{0\\} \\neq \\mathcal{J} \\unlhd \\mathcal{C}$, we have that $\\mathcal{J} \\cap \\mathcal{A} \\neq \\{0\\}$. That is, $\\mathcal{A}$ detects ideals in every intermediate $C^*$-algebra $\\mathcal{A} \\subseteq \\mathcal{C} \\subseteq \\mathcal{B}$. By a result of Pitts and Zarikian, a unital $C^*$-inclusion $\\mathcal{A} \\subseteq \\mathcal{B}$ is hereditarily essential if and only if every pseudo-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.19484","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/2406.19484/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"}