{"paper":{"title":"Chebyshev type inequalities for Hilbert space operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Mohammad Sal Moslehian, Mojtaba Bakherad","submitted_at":"2014-01-08T20:37:31Z","abstract_excerpt":"We establish several operator extensions of the Chebyshev inequality. The main version deals with the Hadamard product of Hilbert space operators. More precisely, we prove that if $\\mathscr{A}$ is a $C^*$-algebra, $T$ is a compact Hausdorff space equipped with a Radon measure $\\mu$, $\\alpha: T\\rightarrow [0, +\\infty)$ is a measurable function and $(A_t)_{t\\in T}, (B_t)_{t\\in T}$ are suitable continuous fields of operators in ${\\mathscr A}$ having the synchronous Hadamard property, then \\begin{align*} \\int_{T} \\alpha(s) d\\mu(s)\\int_{T}\\alpha(t)(A_t\\circ B_t) d\\mu(t)\\geq\\left(\\int_{T}\\alpha(t) A"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.1804","kind":"arxiv","version":2},"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"}