{"paper":{"title":"$A$-numerical radius inequalities for semi-Hilbertian space operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Ali Zamani","submitted_at":"2019-05-10T11:42:26Z","abstract_excerpt":"Let $A$ be a positive bounded operator on a Hilbert space $\\big(\\mathcal{H}, \\langle \\cdot, \\cdot\\rangle \\big)$. The semi-inner product ${\\langle x, y\\rangle}_A := \\langle Ax, y\\rangle$, $x, y\\in\\mathcal{H}$ induces a semi-norm ${\\|\\cdot\\|}_A$ on $\\mathcal{H}$. Let ${\\|T\\|}_A$ and $w_A(T)$ denote the $A$-operator semi-norm and the $A$-numerical radius of an operator $T$ in semi-Hilbertian space $\\big(\\mathcal{H}, {\\|\\cdot\\|}_A\\big)$, respectively. In this paper, we prove the following characterization of $w_A(T)$ \\begin{align*} w_A(T) = \\displaystyle{\\sup_{\\alpha^2 + \\beta^2 = 1}} {\\left\\|\\alp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.04081","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"}