{"paper":{"title":"Numerical radius inequalities involving commutators of $G_{1}$ operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Fuad Kittaneh, Mojtaba Bakherad","submitted_at":"2017-09-05T13:24:58Z","abstract_excerpt":"We prove numerical radius inequalities involving commutators of $G_{1}$ operators and certain analytic functions. Among other inequalities, it is shown that if $A$ and $X$ are bounded linear operators on a complex Hilbert space, then \\begin{equation*} w(f(A)X+X\\bar{f}(A))\\leq {\\frac{2}{d_{A}^{2}}}w(X-AXA^{\\ast }), \\end{equation*} where $A$ is a $G_{1}$ operator with $\\sigma (A)\\subset \\mathbb{D}$ and $f$ is analytic on the unit disk $\\mathbb{D}$ such that $\\textrm{{Re}}(f)>0$ and $f(0)=1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.01850","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"}