{"paper":{"title":"Diagonal dimension and intermediate sub-C*-algebras","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Grigoris Kopsacheilis","submitted_at":"2026-07-27T17:42:04Z","abstract_excerpt":"We show that finiteness of diagonal dimension, in the sense of Li--Liao--Winter, passes to intermediate sub-C*-algebras. More specifically, we obtain an upper bound for the diagonal dimension of the pair of an intermediate sub-C*-algebra in a C*-diagonal together with the diagonal, which we estimate in terms of the diagonal dimension of the ambient pair and the covering dimension of the diagonal's spectrum. This generalizes a theorem of Archbold and Kumjian stating that intermediate sub-C*-algebras of AF-diagonals are AF C*-algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.24699","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/2607.24699/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"}