{"paper":{"title":"Products of C*-algebras that do not embed into the Calkin algebra","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.FA","math.LO"],"primary_cat":"math.OA","authors_text":"Damian G{\\l}odkowski, Piotr Koszmider","submitted_at":"2024-12-15T13:53:32Z","abstract_excerpt":"We consider the Calkin algebra $\\mathcal{Q}(\\ell_2)$, i.e., the quotient of the algebra $\\mathcal B(\\ell_2)$ of all bounded linear operators on the separable Hilbert space $\\ell_2$ divided by the ideal $\\mathcal K(\\ell_2)$ of all compact operators on $\\ell_2$. We show that in the Cohen model of set theory ZFC there is no embedding of the product $(c_0(2^\\omega))^{\\mathbb{N}}$ of infinitely many copies of the abelian C*-algebra $c_0(2^\\omega)$ into $\\mathcal{Q}(\\ell_2)$ (while $c_0(2^\\omega)$ always embeds into $\\mathcal{Q}(\\ell_2)$). This enlarges the collection of the known examples due to Va"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.11191","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/2412.11191/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"}