{"paper":{"title":"Further refinements of generalized numerical radius inequalities for Hilbert space operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mojtaba Bakherad, Monire Hajmohamadi, Rahmatollah Lashkaripour","submitted_at":"2018-05-19T14:04:38Z","abstract_excerpt":"In this paper, we show some refinements of generalized numerical radius inequalities involving the Young and Heinz inequalities. In particular, we present\n  \\begin{align*} w_{p}^{p}(A_{1}^{*}T_{1}B_{1},...,A_{n}^{*}T_{n}B_{n})\\leq\\frac{n^{1-\\frac{1}{r}}}{2^{\\frac{1}{r}}}\\Big\\|\\sum_{i=1}^{n}[B_{i}^{*} f^{2}(|T_{i}|)B_{i}]^{rp}+[A_{i}^{*}g^{2}(|T_{i}^{*}|)A_{i}]^{rp}\\Big\\|^{\\frac{1}{r}} -\\inf_{\\|x\\|=1}\\eta(x), \\end{align*} where $T_{i}, A_{i}, B_{i} \\in {\\mathbb B}({\\mathscr H})\\,\\,(1\\leq i\\leq n)$, $f$ and $g$ are nonnegative continuous functions on $[0, \\infty)$ satisfying $f(t)g(t)=t$ for all"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.07596","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":""},"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"}