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The Berezin number of operator $A$ is defined by $\\mathbf{ber}(A) = \\underset{\\lambda \\in \\Omega}{\\sup} \\big|\\tilde{A}(\\lambda)\\big|=\\underset{\\lambda \\in \\Omega }{\\sup} \\big|\\langle A\\hat{k}_{\\lambd"},"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":"1805.01015","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-02T20:53:58Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"9bc855416c5ec79faa4761f6881e253e5342a2a6da190f21c27fddafbb1267c0","abstract_canon_sha256":"de144d58c2bda1c3ea987a234f6dad258e84a4833008955efbde9e8368fe7ea3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:52.861755Z","signature_b64":"LDag9IDYkH+5PRyo8N49ZSr/j0OqJdFYVRTkC0mI5mnWmAX9XpqO8yMdU+ruZDNMIpXvVjn+HVT7r81pKa/AAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ced7490c22b08bbe414e6d402594c8e04012acddb77bb49e5e99b02140c6a7b","last_reissued_at":"2026-05-18T00:16:52.861067Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:52.861067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some Berezin number inequalities for operator matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Mojtaba Bakherad","submitted_at":"2018-05-02T20:53:58Z","abstract_excerpt":"The Berezin symbol $\\widetilde{A}$ of an operator $A$ acting on the reproducing kernel Hilbert space ${\\mathscr H}={\\mathscr H(}\\Omega)$ over some (non-empty) set is defined by $\\widetilde{A}(\\lambda)=\\langle A\\hat{k}_{\\lambda},\\hat{k}_{\\lambda}\\rangle\\,\\,\\,(\\lambda\\in\\Omega)$, where $\\hat{k}_{\\lambda}=\\frac{{k}_{\\lambda}}{\\|{k}_{\\lambda}\\|}$ is the normalized reproducing kernel of ${\\mathscr H}$. The Berezin number of operator $A$ is defined by $\\mathbf{ber}(A) = \\underset{\\lambda \\in \\Omega}{\\sup} \\big|\\tilde{A}(\\lambda)\\big|=\\underset{\\lambda \\in \\Omega }{\\sup} \\big|\\langle A\\hat{k}_{\\lambd"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.01015","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":"1805.01015","created_at":"2026-05-18T00:16:52.861156+00:00"},{"alias_kind":"arxiv_version","alias_value":"1805.01015v1","created_at":"2026-05-18T00:16:52.861156+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.01015","created_at":"2026-05-18T00:16:52.861156+00:00"},{"alias_kind":"pith_short_12","alias_value":"PTWXJEGCFMEL","created_at":"2026-05-18T12:32:46.962924+00:00"},{"alias_kind":"pith_short_16","alias_value":"PTWXJEGCFMELXZAU","created_at":"2026-05-18T12:32:46.962924+00:00"},{"alias_kind":"pith_short_8","alias_value":"PTWXJEGC","created_at":"2026-05-18T12:32:46.962924+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/PTWXJEGCFMELXZAU43KAEWKMRY","json":"https://pith.science/pith/PTWXJEGCFMELXZAU43KAEWKMRY.json","graph_json":"https://pith.science/api/pith-number/PTWXJEGCFMELXZAU43KAEWKMRY/graph.json","events_json":"https://pith.science/api/pith-number/PTWXJEGCFMELXZAU43KAEWKMRY/events.json","paper":"https://pith.science/paper/PTWXJEGC"},"agent_actions":{"view_html":"https://pith.science/pith/PTWXJEGCFMELXZAU43KAEWKMRY","download_json":"https://pith.science/pith/PTWXJEGCFMELXZAU43KAEWKMRY.json","view_paper":"https://pith.science/paper/PTWXJEGC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1805.01015&json=true","fetch_graph":"https://pith.science/api/pith-number/PTWXJEGCFMELXZAU43KAEWKMRY/graph.json","fetch_events":"https://pith.science/api/pith-number/PTWXJEGCFMELXZAU43KAEWKMRY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PTWXJEGCFMELXZAU43KAEWKMRY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PTWXJEGCFMELXZAU43KAEWKMRY/action/storage_attestation","attest_author":"https://pith.science/pith/PTWXJEGCFMELXZAU43KAEWKMRY/action/author_attestation","sign_citation":"https://pith.science/pith/PTWXJEGCFMELXZAU43KAEWKMRY/action/citation_signature","submit_replication":"https://pith.science/pith/PTWXJEGCFMELXZAU43KAEWKMRY/action/replication_record"}},"created_at":"2026-05-18T00:16:52.861156+00:00","updated_at":"2026-05-18T00:16:52.861156+00:00"}