{"paper":{"title":"Further Inequalities for the Numerical Radius of Hilbert Space Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"H. R. Moradi, P. Harikrishnan, S. Furuichi, S. Tafazoli","submitted_at":"2019-07-13T03:20:00Z","abstract_excerpt":"In this article, we present some new inequalities for numerical radius of Hilbert space operators via convex functions. Our results generalize and improve earlier results by El-Haddad and Kittaneh. Among several results, we show that if $A\\in \\mathbb{B}\\left( \\mathcal{H} \\right)$ and $r\\ge 2$, then \\[{{w}^{r}}\\left( A \\right)\\le {{\\left\\| A \\right\\|}^{r}}-\\underset{\\left\\| x \\right\\|=1}{\\mathop{\\inf }}\\,{{\\left\\| {{\\left| \\left| A \\right|-w\\left( A \\right) \\right|}^{\\frac{r}{2}}}x \\right\\|}^{2}}\\] where $w\\left( \\cdot \\right)$ and $\\left\\| \\cdot \\right\\|$ denote the numerical radius and usual "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.06003","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"}