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Lin [Studia Math. 2013;215:187-194]. In particular, we show the operator inequality\n  \\begin{eqnarray*} \\Phi^p\\left(A\\nabla_\\nu B+2rMm(A^{-1}\\nabla B^{-1}-A^{-1}\\sharp B^{-1})\\right)\\leq\\alpha^p\\Phi^p\\left(A\\sharp_\\nu B\\right), \\end{eqnarray*} where $A,B$ are positive operators on a Hilbert space such that $0<m \\leq A, B \\leq M$ for some positive numbers $m, M$, $\\Phi$ is a positive unital linear map, $\\nu\\in[0,1]$, $r=\\min\\{\\nu,1-\\nu\\}$, $p>0$ and $\\alpha=\\max\\left\\{\\frac{(M+m)^2}{4Mm},\\frac{(M+m)^2}{4^\\frac{2}{p}Mm}\\r","authors_text":"Mojtaba Bakherad","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-06-21T21:01:27Z","title":"Refinements of a reversed AM-GM operator inequality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06414","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:1c5c47929e7de4e293e96d976ac303ae1952c6552cb8b12577d10ddc4d195991","target":"record","created_at":"2026-05-18T00:33:32Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"6352fbab1fe51a1a41efcd0ed4c8dacbbc6b936c7151884c849751262ac15837","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-06-21T21:01:27Z","title_canon_sha256":"8e9eebc6e2943abe378613f42d92b5f812832f2353394e3f7b3f053f1ef6807c"},"schema_version":"1.0","source":{"id":"1506.06414","kind":"arxiv","version":1}},"canonical_sha256":"cc879ba955d6f027312a8ec899f08f39c6694a16a89423f8512f9db35e102087","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cc879ba955d6f027312a8ec899f08f39c6694a16a89423f8512f9db35e102087","first_computed_at":"2026-05-18T00:33:32.811643Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:32.811643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jn2AuIech9OH1EO7PtMFsTzawBdavCCw5XcdTRiEF2dvB39J/R08YbD8aYOXS3GVEZfgj5teoMlSnoKacwKYDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:32.812303Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.06414","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c5c47929e7de4e293e96d976ac303ae1952c6552cb8b12577d10ddc4d195991","sha256:7aab03ede49106116f4b078f0031fdc94e5e51cd02fbf0fe8cff7d9495caaa57"],"state_sha256":"2abdde7974b8f042d2f3598a1d23748880ccc5d773e4eb852346637b47f82f5a"}