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Let ${\\|T\\|}_A$ and $w_A(T)$ denote the $A$-operator semi-norm and the $A$-numerical radius of an operator $T$ in semi-Hilbertian space $\\big(\\mathcal{H}, {\\|\\cdot\\|}_A\\big)$, respectively. In this paper, we prove the following characterization of $w_A(T)$ \\begin{align*} w_A(T) = \\displaystyle{\\sup_{\\alpha^2 + \\beta^2 = 1}} {\\left\\|\\alp"},"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":"1905.04081","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-05-10T11:42:26Z","cross_cats_sorted":[],"title_canon_sha256":"8587004b07cc2f41a3eafd17f2707f456d2723ace9e754589367298f6e3da21a","abstract_canon_sha256":"5fe8c980296271609a291112f4f3010dfd5c723d5409a8fc8732716393a6a873"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:34.643540Z","signature_b64":"Ws1UEN7IiczhReYimgNXmSwX3N4sL3ER8cD5gu+piv+7lnDaFDGX2/Mp5q+6wPbHoGBhhRXAIeA0sMYiZ4Y1CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"42d88893cbd9c9f28d7a12ad55bef2a31162d8b9bf25e89a2dde8964633a5123","last_reissued_at":"2026-05-17T23:46:34.642907Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:34.642907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$A$-numerical radius inequalities for semi-Hilbertian space operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Ali Zamani","submitted_at":"2019-05-10T11:42:26Z","abstract_excerpt":"Let $A$ be a positive bounded operator on a Hilbert space $\\big(\\mathcal{H}, \\langle \\cdot, \\cdot\\rangle \\big)$. The semi-inner product ${\\langle x, y\\rangle}_A := \\langle Ax, y\\rangle$, $x, y\\in\\mathcal{H}$ induces a semi-norm ${\\|\\cdot\\|}_A$ on $\\mathcal{H}$. Let ${\\|T\\|}_A$ and $w_A(T)$ denote the $A$-operator semi-norm and the $A$-numerical radius of an operator $T$ in semi-Hilbertian space $\\big(\\mathcal{H}, {\\|\\cdot\\|}_A\\big)$, respectively. In this paper, we prove the following characterization of $w_A(T)$ \\begin{align*} w_A(T) = \\displaystyle{\\sup_{\\alpha^2 + \\beta^2 = 1}} {\\left\\|\\alp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.04081","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1905.04081","created_at":"2026-05-17T23:46:34.643006+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.04081v1","created_at":"2026-05-17T23:46:34.643006+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.04081","created_at":"2026-05-17T23:46:34.643006+00:00"},{"alias_kind":"pith_short_12","alias_value":"ILMIRE6L3HE7","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_16","alias_value":"ILMIRE6L3HE7FDL2","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_8","alias_value":"ILMIRE6L","created_at":"2026-05-18T12:33:18.533446+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ILMIRE6L3HE7FDL2CKWVLPXSUM","json":"https://pith.science/pith/ILMIRE6L3HE7FDL2CKWVLPXSUM.json","graph_json":"https://pith.science/api/pith-number/ILMIRE6L3HE7FDL2CKWVLPXSUM/graph.json","events_json":"https://pith.science/api/pith-number/ILMIRE6L3HE7FDL2CKWVLPXSUM/events.json","paper":"https://pith.science/paper/ILMIRE6L"},"agent_actions":{"view_html":"https://pith.science/pith/ILMIRE6L3HE7FDL2CKWVLPXSUM","download_json":"https://pith.science/pith/ILMIRE6L3HE7FDL2CKWVLPXSUM.json","view_paper":"https://pith.science/paper/ILMIRE6L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.04081&json=true","fetch_graph":"https://pith.science/api/pith-number/ILMIRE6L3HE7FDL2CKWVLPXSUM/graph.json","fetch_events":"https://pith.science/api/pith-number/ILMIRE6L3HE7FDL2CKWVLPXSUM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ILMIRE6L3HE7FDL2CKWVLPXSUM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ILMIRE6L3HE7FDL2CKWVLPXSUM/action/storage_attestation","attest_author":"https://pith.science/pith/ILMIRE6L3HE7FDL2CKWVLPXSUM/action/author_attestation","sign_citation":"https://pith.science/pith/ILMIRE6L3HE7FDL2CKWVLPXSUM/action/citation_signature","submit_replication":"https://pith.science/pith/ILMIRE6L3HE7FDL2CKWVLPXSUM/action/replication_record"}},"created_at":"2026-05-17T23:46:34.643006+00:00","updated_at":"2026-05-17T23:46:34.643006+00:00"}