{"paper":{"title":"$q$-numerical radius of rank-one operators and the generalized Buzano inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Du\\v{s}an Den\\v{c}i\\'c, Hranislav Stankovi\\'c, Ivan Damnjanovi\\'c, Mihailo Krsti\\'c","submitted_at":"2025-03-06T23:22:19Z","abstract_excerpt":"Here, we study the $q$-numerical radius of rank-one operators on a Hilbert space $\\mathcal{H}$. More precisely, for $q \\in [0,1]$ and $a, b \\in \\mathcal{H}$, we establish the formula \\[ \\omega_q(a \\otimes b) = \\frac{1}{2}\\left(\\|a\\|\\|b\\| + q|\\langle a, b \\rangle| + \\sqrt{1-q^2}\\sqrt{\\|a\\|^2\\|b\\|^2 - |\\langle a, b \\rangle|^2}\\right), \\] which represents a generalization of the well-known formula for the numerical radius of a rank-one operator in a Hilbert space, obtained by setting $q = 1$. As a corollary, we also derive a generalization of the classical Buzano inequality."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.05036","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/2503.05036/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"}