{"paper":{"title":"Selfless C*-correspondences, operator valued C*-probability spaces and completely positive maps","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"David Gao, Gregory Patchell, Leonel Robert, Marius Junge, Srivatsav Kunnawalkam Elayavalli","submitted_at":"2026-07-22T16:51:01Z","abstract_excerpt":"We develop a general theory of selflessness for C*-correspondences, with several applications. Specializing this theory to completely positive maps, in particular to conditional expectations, gives rise to a novel notion of relative selflessness. Among applications, the machinery developed here yields new examples of selfless C*-algebras, for instance among minimal tensor products and reduced crossed products, new examples of MF C*-algebras arising as reduced amalgamated free products, a conceptually new proof of Kirchberg's $\\mathcal{O}_{\\infty}$-absorption theorem, and the lack of ``phantom'"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.20361","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/2607.20361/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"}