{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:5SKLR3VJNOL7BTHY4BYHRJTVYC","short_pith_number":"pith:5SKLR3VJ","schema_version":"1.0","canonical_sha256":"ec94b8eea96b97f0ccf8e07078a675c0820a6d7af8b4f59e9cfbc48c3cb48c14","source":{"kind":"arxiv","id":"1403.6431","version":2},"attestation_state":"computed","paper":{"title":"Bounded holomorphic functions attaining their norms in the bidual","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Daniel Carando, Martin Mazzitelli","submitted_at":"2014-03-25T17:33:41Z","abstract_excerpt":"Under certain hypotheses on the Banach space $X$, we prove that the set of analytic functions in $\\mathcal{A}_u(X)$ (the algebra of all holomorphic and uniformly continuous functions in the ball of $X$) whose Aron-Berner extensions attain their norms, is dense in $\\mathcal{A}_u(X)$. The result holds also for functions with values in a dual space or in a Banach space with the so-called property $(\\beta)$. For this, we establish first a Lindenstrauss type theorem for continuous polynomials. We also present some counterexamples for the Bishop-Phelps theorem in the analytic and polynomial cases wh"},"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":"1403.6431","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-03-25T17:33:41Z","cross_cats_sorted":[],"title_canon_sha256":"322d426cf5cd48389173b875e39efae4cf154ab41efb7fde1329dcf7132ed964","abstract_canon_sha256":"a56b273999faf5265b5d940c0e69b2d25bc44e0bbec1d31d2ced7e918665ea9b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:19:36.244049Z","signature_b64":"Mxo/FbGdsj2YJwySMR0evbZalOy/VnXeZGR76ZTbZEW7nQ6ezHM/4EwIzmaOzIbKBeOURgH+WSqm2M4n8SIgDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec94b8eea96b97f0ccf8e07078a675c0820a6d7af8b4f59e9cfbc48c3cb48c14","last_reissued_at":"2026-05-18T02:19:36.243407Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:19:36.243407Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bounded holomorphic functions attaining their norms in the bidual","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Daniel Carando, Martin Mazzitelli","submitted_at":"2014-03-25T17:33:41Z","abstract_excerpt":"Under certain hypotheses on the Banach space $X$, we prove that the set of analytic functions in $\\mathcal{A}_u(X)$ (the algebra of all holomorphic and uniformly continuous functions in the ball of $X$) whose Aron-Berner extensions attain their norms, is dense in $\\mathcal{A}_u(X)$. The result holds also for functions with values in a dual space or in a Banach space with the so-called property $(\\beta)$. For this, we establish first a Lindenstrauss type theorem for continuous polynomials. We also present some counterexamples for the Bishop-Phelps theorem in the analytic and polynomial cases wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.6431","kind":"arxiv","version":2},"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":"1403.6431","created_at":"2026-05-18T02:19:36.243498+00:00"},{"alias_kind":"arxiv_version","alias_value":"1403.6431v2","created_at":"2026-05-18T02:19:36.243498+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.6431","created_at":"2026-05-18T02:19:36.243498+00:00"},{"alias_kind":"pith_short_12","alias_value":"5SKLR3VJNOL7","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_16","alias_value":"5SKLR3VJNOL7BTHY","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_8","alias_value":"5SKLR3VJ","created_at":"2026-05-18T12:28:14.216126+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/5SKLR3VJNOL7BTHY4BYHRJTVYC","json":"https://pith.science/pith/5SKLR3VJNOL7BTHY4BYHRJTVYC.json","graph_json":"https://pith.science/api/pith-number/5SKLR3VJNOL7BTHY4BYHRJTVYC/graph.json","events_json":"https://pith.science/api/pith-number/5SKLR3VJNOL7BTHY4BYHRJTVYC/events.json","paper":"https://pith.science/paper/5SKLR3VJ"},"agent_actions":{"view_html":"https://pith.science/pith/5SKLR3VJNOL7BTHY4BYHRJTVYC","download_json":"https://pith.science/pith/5SKLR3VJNOL7BTHY4BYHRJTVYC.json","view_paper":"https://pith.science/paper/5SKLR3VJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1403.6431&json=true","fetch_graph":"https://pith.science/api/pith-number/5SKLR3VJNOL7BTHY4BYHRJTVYC/graph.json","fetch_events":"https://pith.science/api/pith-number/5SKLR3VJNOL7BTHY4BYHRJTVYC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5SKLR3VJNOL7BTHY4BYHRJTVYC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5SKLR3VJNOL7BTHY4BYHRJTVYC/action/storage_attestation","attest_author":"https://pith.science/pith/5SKLR3VJNOL7BTHY4BYHRJTVYC/action/author_attestation","sign_citation":"https://pith.science/pith/5SKLR3VJNOL7BTHY4BYHRJTVYC/action/citation_signature","submit_replication":"https://pith.science/pith/5SKLR3VJNOL7BTHY4BYHRJTVYC/action/replication_record"}},"created_at":"2026-05-18T02:19:36.243498+00:00","updated_at":"2026-05-18T02:19:36.243498+00:00"}