{"paper":{"title":"Estimates of operator moduli of continuity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.CV","math.SP"],"primary_cat":"math.FA","authors_text":"Aleksei Aleksandrov, Vladimir Peller","submitted_at":"2011-04-18T18:11:36Z","abstract_excerpt":"In \\cite{AP2} we obtained general estimates of the operator moduli of continuity of functions on the real line. In this paper we improve the estimates obtained in \\cite{AP2} for certain special classes of functions.\n  In particular, we improve estimates of Kato \\cite{Ka} and show that $$ \\big\\|\\,|S|-|T|\\,\\big\\|\\le C\\|S-T\\|\\log(2+\\log\\frac{\\|S\\|+\\|T\\|}{\\|S-T\\|}) $$ for every bounded operators $S$ and $T$ on Hilbert space. Here $|S|\\df(S^*S)^{1/2}$. Moreover, we show that this inequality is sharp.\n  We prove in this paper that if $f$ is a nondecreasing continuous function on $\\R$ that vanishes o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3553","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"}