{"paper":{"title":"On the convexity of Berezin range and Berezin radius inequalities via a class of semi-norms","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Athul Augustine, P. Hiran Das, Pintu Bhunia, P. Shankar","submitted_at":"2025-07-30T07:12:16Z","abstract_excerpt":"This paper introduces a new family of semi-norms, say $\\sigma_\\mu$-Berezin norm on the space of all bounded linear operators $B(\\mathcal{H})$ defined on a reproducing kernel Hilbert space $\\mathcal{H}$, namely, for each $\\mu \\in [0,1]$ and $p\\geq 1$, $$\\|T\\|_{\\sigma_{\\mu}\\text{-ber}}= \\sup_{\\lambda\\in\\Omega}\\left\\lbrace \\left(|\\langle T\\hat{k}_\\lambda,\\hat{k}_\\lambda\\rangle |^p~ \\sigma_{\\mu}~ \\|T\\hat{k}_\\lambda\\|^p\\right)^{\\frac{1}{p}}\\right\\rbrace $$ where $T\\in B(\\mathcal{H})$ and $\\sigma_{\\mu}$ is an interpolation path of the symmetric mean $\\sigma$. We investigate many fundamental properti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.22427","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/2507.22427/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"}