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Among other inequalities, it is shown that if $A, B, X$ are $n\\times n$ matrices, then \\begin{align*} \\|AXB^*\\|^2\\leq\\|f_1(A^*A)Xg_1(B^*B)\\|\\,\\|f_2(A^*A)Xg_2(B^*B)\\|, \\end{align*} where $f_1,f_2,g_1,g_2$ are non-negative continues functions such that $f_1(t)f_2(t)=t$ and $g_1(t)g_2(t)=t\\,\\,(t\\geq0)$. We also obtain the inequality \\begin{align*} \\left|\\left|\\left|AB^*\\right|\\right|\\right|^2\\nonumber&\\leq \\left|\\left|\\left|p(A^*A)^{\\frac{m}{p}}+ (1-p)(B^*B)^{\\frac{s}{1-p}}\\right|\\right|\\","authors_text":"Mojtaba Bakherad, Monire Hajmohamadi, Rahmatollah Lashkaripour","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-08-19T15:23:28Z","title":"Extensions of interpolation between the arithmetic-geometric mean inequality for matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.05862","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":"sha256:19a70223c5b73c4bfc950d80f154b6c25775c3c3a8b415132584786bc9816b67","target":"record","created_at":"2026-05-18T00:33:31Z","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":"9ea6eb36eae0e1728b81f18537a2bd57ecb640310cdd4866f1226386eee21e3f","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-08-19T15:23:28Z","title_canon_sha256":"21f70777dea490f95c2b5461891b341a688ec8c7623a88b4f2a6d34d0d405776"},"schema_version":"1.0","source":{"id":"1708.05862","kind":"arxiv","version":1}},"canonical_sha256":"b871919d01f6fa7e2b3f8dc960923a534fd49a3aa23247f554a54578b5996f16","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b871919d01f6fa7e2b3f8dc960923a534fd49a3aa23247f554a54578b5996f16","first_computed_at":"2026-05-18T00:33:31.740464Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:31.740464Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7BCJmGsDJZDC3GraLF0MOQ1uOOgTFMQB3j2jpLKhQT4s15GsRxDyXbJI+iM4E33C5wL82arp0l5qhPJJM3miDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:31.741074Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.05862","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:19a70223c5b73c4bfc950d80f154b6c25775c3c3a8b415132584786bc9816b67","sha256:59bed7d67d7d01ebcdc8685b7e60ead6fb5f002c1dc239bad150ff6923e3f8a6"],"state_sha256":"ef33a0fa26566aed5e41cf927f9685745ea4d477b1371ab48ed68289c64e6dc1"}