{"paper":{"title":"Convexity of the Berezin range of finite rank operators","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Athul Augustine, M. Garayev, P. Shankar","submitted_at":"2024-11-16T10:40:04Z","abstract_excerpt":"For a bounded linear operator $T$ acting on a reproducing kernel Hilbert space $\\mathcal{H}(\\Omega)$ over a nonempty set $\\Omega$, the Berezin range of $T$ is defined by \\[ \\mathrm{Ber}(T)=\\left\\{\\langle T\\hat{k}_{\\lambda},\\hat{k}_{\\lambda}\\rangle_{\\mathcal{H}} : \\lambda \\in \\Omega \\right\\} \\] and the Berezin radius is given by \\[ \\mathrm{ber}(T)=\\sup\\left\\{ |\\gamma| : \\gamma \\in \\mathrm{Ber}(T) \\right\\}, \\] where $\\hat{k}_{\\lambda}$ denotes the normalized reproducing kernel at $\\lambda \\in \\Omega$. In this paper, we study the convexity of the Berezin range of finite rank operators on the Hard"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.10771","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/2411.10771/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"}