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In particular, we prove \\begin{align*} \\|f(A)Xg(B)\\pm g(B)Xf(A)\\|_2\\leq \\left\\|\\frac{(I+|A|)X(I+|B|)+(I+|B|)X(I+|A|)}{d_Ad_B}\\right\\|_2, \\end{align*} where $A, B, X\\in\\mathbb{M}_n$ such that $A$, $B$ are Hermitian with $\\sigma (A)\\cup\\sigma(B)\\subset\\mathbb{D}$ and $f, g$ are analytic on the complex unit disk $\\mathbb{{D}}$, $g(0)=f(0)=1$, $\\textrm{Re}(f)>0$ and $\\textrm{Re}(g)>0$."},"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":"1801.02934","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-01-09T13:47:49Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"96dd87431578869436d571d6a5cef1ca4968d85181a4324079f7de0fb353da4f","abstract_canon_sha256":"ecafca56fbbff2c57506bb1ab6ff87231e2da98893a1a903ee36eaedf072dbde"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:21.994040Z","signature_b64":"FG7iK6m3GDusOqTcmSHMTNJVQzuRgqvNXmNU340yU3CxyV1KtXmaSV4C2slckBtFZcaiemxeqR+i0v65MwIbAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"582fb235e3c621b20bc5aecf00791e40323432922165f04907035df05e8333e7","last_reissued_at":"2026-05-18T00:26:21.993421Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:21.993421Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Unitarily invariant norm inequalities involving $G_1$ operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Mojtaba Bakherad","submitted_at":"2018-01-09T13:47:49Z","abstract_excerpt":"In this paper, we present some upper bounds for unitarily invariant norms inequalities. 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