{"paper":{"title":"Some generalized numerical radius inequalities for Hilbert space operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA","math.SP"],"primary_cat":"math.FA","authors_text":"Mohammad Sal Moslehian, Mostafa Sattari, Takeaki Yamazaki","submitted_at":"2014-09-01T08:25:52Z","abstract_excerpt":"We generalize several inequalities involving powers of the numerical radius for product of two operators acting on a Hilbert space. For any $A, B, X\\in \\mathbb{B}(\\mathscr{H})$ such that $A,B$ are positive, we establish some numerical radius inequalities for $A^\\alpha XB^\\alpha$ and $A^\\alpha X B^{1-\\alpha}\\,\\,(0 \\leq \\alpha \\leq 1)$ and Heinz means under mild conditions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0321","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"}