{"paper":{"title":"Operator norm and numerical radius analogues of Cohen's inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Roman Drnov\\v{s}ek","submitted_at":"2019-05-20T11:48:28Z","abstract_excerpt":"Let $D$ be an invertible multiplication operator on $L^2(X, \\mu)$, and let $A$ be a bounded operator on $L^2(X, \\mu)$. In this note we prove that $\\|A\\|^2 \\le \\|D A\\| \\, \\|D^{-1} A\\|$, where $\\|\\cdot\\|$ denotes the operator norm. If, in addition, the operators $A$ and $D$ are positive, we also have $w(A)^2 \\le w(D A) \\, w(D^{-1} A)$, where $w$ denotes the numerical radius."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.08009","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"}