{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:Q7KYBIOWF5PVZ3KPST6QRRFBII","short_pith_number":"pith:Q7KYBIOW","schema_version":"1.0","canonical_sha256":"87d580a1d62f5f5ced4f94fd08c4a1420ca37043c0d4f2a587c34924c88bde34","source":{"kind":"arxiv","id":"1706.04497","version":1},"attestation_state":"computed","paper":{"title":"Upper bounds for numerical radius inequalities involving off-diagonal operator matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Khalid Shebrawi, Mojtaba Bakherad","submitted_at":"2017-06-14T13:58:07Z","abstract_excerpt":"In this paper, we establish some upper bounds for numerical radius inequalities including of $2\\times 2$ operator matrices and their off-diagonal parts. Among other inequalities, it is shown that if $T=\\left[\\begin{array}{cc}\n  0&X,\n  Y&0\n  \\end{array}\\right]$, then\n  \\begin{align*}\n  \\omega^{r}(T)\\leq 2^{r-2}\\left\\|f^{2r}(|X|)+g^{2r}(|Y^*|)\\right\\|^\\frac{1}{2}\\left\\|f^{2r}(|Y|)+g^{2r}(|X^*|)\\right\\|^\\frac{1}{2}\n  \\end{align*} and\n  \\begin{align*}\n  \\omega^{r}(T)\\leq 2^{r-2}\\left\\|f^{2r}(|X|)+f^{2r}(|Y^*|)\\right\\|^\\frac{1}{2}\\left\\|g^{2r}(|Y|)+g^{2r}(|X^*|)\\right\\|^\\frac{1}{2},\n  \\end{align*} "},"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":"1706.04497","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-14T13:58:07Z","cross_cats_sorted":[],"title_canon_sha256":"97ba888083c53aa258a764cfab1fd3bf5052f4cadf3b7838689712c6c7609ef8","abstract_canon_sha256":"e4b5e6b5dc3e3ac3b9cde79db414d7bf27ee57d15b10f9368e08855c5e55b163"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:45.951124Z","signature_b64":"O7H3+ILlTER5QpBbiuTHojxpPLdv5ZEnr3dPPaIzI2AurlXdb0xmE1B4nUxCqd3k/l5mrOWHFyyHxH8Hin5nCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"87d580a1d62f5f5ced4f94fd08c4a1420ca37043c0d4f2a587c34924c88bde34","last_reissued_at":"2026-05-18T00:00:45.950752Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:45.950752Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Upper bounds for numerical radius inequalities involving off-diagonal operator matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Khalid Shebrawi, Mojtaba Bakherad","submitted_at":"2017-06-14T13:58:07Z","abstract_excerpt":"In this paper, we establish some upper bounds for numerical radius inequalities including of $2\\times 2$ operator matrices and their off-diagonal parts. Among other inequalities, it is shown that if $T=\\left[\\begin{array}{cc}\n  0&X,\n  Y&0\n  \\end{array}\\right]$, then\n  \\begin{align*}\n  \\omega^{r}(T)\\leq 2^{r-2}\\left\\|f^{2r}(|X|)+g^{2r}(|Y^*|)\\right\\|^\\frac{1}{2}\\left\\|f^{2r}(|Y|)+g^{2r}(|X^*|)\\right\\|^\\frac{1}{2}\n  \\end{align*} and\n  \\begin{align*}\n  \\omega^{r}(T)\\leq 2^{r-2}\\left\\|f^{2r}(|X|)+f^{2r}(|Y^*|)\\right\\|^\\frac{1}{2}\\left\\|g^{2r}(|Y|)+g^{2r}(|X^*|)\\right\\|^\\frac{1}{2},\n  \\end{align*} "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.04497","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":"1706.04497","created_at":"2026-05-18T00:00:45.950806+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.04497v1","created_at":"2026-05-18T00:00:45.950806+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.04497","created_at":"2026-05-18T00:00:45.950806+00:00"},{"alias_kind":"pith_short_12","alias_value":"Q7KYBIOWF5PV","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_16","alias_value":"Q7KYBIOWF5PVZ3KP","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_8","alias_value":"Q7KYBIOW","created_at":"2026-05-18T12:31:37.085036+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/Q7KYBIOWF5PVZ3KPST6QRRFBII","json":"https://pith.science/pith/Q7KYBIOWF5PVZ3KPST6QRRFBII.json","graph_json":"https://pith.science/api/pith-number/Q7KYBIOWF5PVZ3KPST6QRRFBII/graph.json","events_json":"https://pith.science/api/pith-number/Q7KYBIOWF5PVZ3KPST6QRRFBII/events.json","paper":"https://pith.science/paper/Q7KYBIOW"},"agent_actions":{"view_html":"https://pith.science/pith/Q7KYBIOWF5PVZ3KPST6QRRFBII","download_json":"https://pith.science/pith/Q7KYBIOWF5PVZ3KPST6QRRFBII.json","view_paper":"https://pith.science/paper/Q7KYBIOW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.04497&json=true","fetch_graph":"https://pith.science/api/pith-number/Q7KYBIOWF5PVZ3KPST6QRRFBII/graph.json","fetch_events":"https://pith.science/api/pith-number/Q7KYBIOWF5PVZ3KPST6QRRFBII/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Q7KYBIOWF5PVZ3KPST6QRRFBII/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Q7KYBIOWF5PVZ3KPST6QRRFBII/action/storage_attestation","attest_author":"https://pith.science/pith/Q7KYBIOWF5PVZ3KPST6QRRFBII/action/author_attestation","sign_citation":"https://pith.science/pith/Q7KYBIOWF5PVZ3KPST6QRRFBII/action/citation_signature","submit_replication":"https://pith.science/pith/Q7KYBIOWF5PVZ3KPST6QRRFBII/action/replication_record"}},"created_at":"2026-05-18T00:00:45.950806+00:00","updated_at":"2026-05-18T00:00:45.950806+00:00"}