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Then for every unital positive linear map $\\Phi$, \\[\\Phi(A^{-1})^2\\le (\\frac{(M+m)^2}{4Mm})^2\\Phi(A)^{-2}.\\] As a consequence, \\[\\Phi(A^{-1})\\Phi(A)+\\Phi(A)\\Phi(A^{-1}) \\le \\frac{(M+m)^2}{2Mm}.\\]"},"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":"1212.5690","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-12-22T13:40:21Z","cross_cats_sorted":[],"title_canon_sha256":"c31f07fa740d9f4d526aef09d7e56d58474eb190e9675f7de3f6e434a52892b8","abstract_canon_sha256":"3e1529247b89717e8fb9d9f98fc5734c9d3e18e3b2aaa45b32591944f4ddb812"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:37:51.749529Z","signature_b64":"0dDDt30R3L7UyOAJXSCUbr/HzQh1l2064BIgqr9EUhCv/rAocC1xW4BEquvi7BPRM+GeyihkAzlCDZIllADcCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c3e33c60d0950e626ac82c619e33fef7a0185158ff61695f7fea50148207e7c","last_reissued_at":"2026-05-18T03:37:51.748806Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:37:51.748806Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On an operator Kantorovich inequality for positive linear maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Minghua Lin","submitted_at":"2012-12-22T13:40:21Z","abstract_excerpt":"We improve the operator Kantorovich inequality as follows: Let $A$ be a positive operator on a Hilbert space with $0<m\\le A \\le M$. 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