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Among other inequalities, it is shown that if\n  ${\\mathfrak A}$ is a $C^*$-algebra, $T$ is a compact Hausdorff space equipped with a Radon measure $\\mu$ as a totaly order set, then \\begin{align*} \\int_{T} \\alpha(s) d\\mu(s)\\int_{T}\\alpha(t)(A_t\\circ B_t) d\\mu(t)\\geq\\Big{(}\\int_{T}\\alpha(t) (A_tm_{r,\\alpha} B_t) d\\mu(t)\\Big{)}\\circ\\Big{(}\\int_{T}\\alpha(s) (A_sm_{r,1-\\alpha} B_s) d\\mu(s)\\Big{)}, \\end{align*} wher"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1806.05883","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-06-15T10:11:30Z","cross_cats_sorted":[],"title_canon_sha256":"402d2be26dc5b8463a24208881d3af6e3a10fc541bb0311c16156a69578fdff4","abstract_canon_sha256":"eb0ce2e7725feb948e1ae6d697a996a541b196e2c3deb019ecf1fc814d5d1f52"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:09.161868Z","signature_b64":"Byh0/gsWQgslAYCI8+/DRja1MinVjKXdVqpBORnFZhr/0cZhjyHWhEVMIndgRSXhI69t91FYdcH77yNUvJE/Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c51787899909b45782aaab1274722fe8b80b32a37805c022655429cb6ff3167","last_reissued_at":"2026-05-18T00:13:09.161234Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:09.161234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Noncommutative Chebyshev inequality involving the Hadamard product","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mojtaba Bakherad, Silvestru Sever Dragomir","submitted_at":"2018-06-15T10:11:30Z","abstract_excerpt":"We present several operator extensions of the Chebyshev inequality for Hilbert space operators. 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