{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1994:IJN7UQ36OLJWB42KZRSV6J522O","short_pith_number":"pith:IJN7UQ36","schema_version":"1.0","canonical_sha256":"425bfa437e72d360f34acc655f27bad3a63f46c5866a843ed0f3a9c66019ace7","source":{"kind":"arxiv","id":"math/9401206","version":1},"attestation_state":"computed","paper":{"title":"Q-Reflexive Banach spaces","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Richard M. Aron, Sean Dineen","submitted_at":"1994-01-05T00:00:00Z","abstract_excerpt":"Let $E$ be a Banach space and, for any positive integer $n$, let ${\\cal P}(^nE)$ denote the Banach space of continuous $n$-homogeneous polynomials on $E$. Davie and Gamelin showed that the natural extension mapping from ${\\cal P}(^nE)$ to ${\\cal P}(^nE^{\\ast\\ast})$ is an isometry into the latter space. Here, we investigate when there is a natural isomorphism between ${\\cal P}(^nE)^{\\ast\\ast}$ and ${\\cal P}(^nE^{\\ast\\ast})$. Among other things, we show that if $E$ satisfies: \\break (a) no spreading model built on a normalised weakly null sequence has a lower $q$-estimate for any $q < \\infty,$ ("},"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":"math/9401206","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.FA","submitted_at":"1994-01-05T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"556bac93a33d13968b55c1eba98b9c4fd6269c4fd91989639822cf30996a54ad","abstract_canon_sha256":"6081d5c5716938b18c9f79d653c935d1286ec31d3b7b380a1630bd0d44b3df89"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:51.728236Z","signature_b64":"/XLEZvMgDaXQuoyc0jPg1/7LQjbAdfm4l9tytir7Cus7bYBq2GhphG3Mhdy7PtKA5LheFJuXmuH5I7gvqyzpCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"425bfa437e72d360f34acc655f27bad3a63f46c5866a843ed0f3a9c66019ace7","last_reissued_at":"2026-05-18T01:05:51.727829Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:51.727829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Q-Reflexive Banach spaces","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Richard M. Aron, Sean Dineen","submitted_at":"1994-01-05T00:00:00Z","abstract_excerpt":"Let $E$ be a Banach space and, for any positive integer $n$, let ${\\cal P}(^nE)$ denote the Banach space of continuous $n$-homogeneous polynomials on $E$. Davie and Gamelin showed that the natural extension mapping from ${\\cal P}(^nE)$ to ${\\cal P}(^nE^{\\ast\\ast})$ is an isometry into the latter space. Here, we investigate when there is a natural isomorphism between ${\\cal P}(^nE)^{\\ast\\ast}$ and ${\\cal P}(^nE^{\\ast\\ast})$. Among other things, we show that if $E$ satisfies: \\break (a) no spreading model built on a normalised weakly null sequence has a lower $q$-estimate for any $q < \\infty,$ ("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9401206","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":"math/9401206","created_at":"2026-05-18T01:05:51.727896+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/9401206v1","created_at":"2026-05-18T01:05:51.727896+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9401206","created_at":"2026-05-18T01:05:51.727896+00:00"},{"alias_kind":"pith_short_12","alias_value":"IJN7UQ36OLJW","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_16","alias_value":"IJN7UQ36OLJWB42K","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_8","alias_value":"IJN7UQ36","created_at":"2026-05-18T12:25:47.102015+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/IJN7UQ36OLJWB42KZRSV6J522O","json":"https://pith.science/pith/IJN7UQ36OLJWB42KZRSV6J522O.json","graph_json":"https://pith.science/api/pith-number/IJN7UQ36OLJWB42KZRSV6J522O/graph.json","events_json":"https://pith.science/api/pith-number/IJN7UQ36OLJWB42KZRSV6J522O/events.json","paper":"https://pith.science/paper/IJN7UQ36"},"agent_actions":{"view_html":"https://pith.science/pith/IJN7UQ36OLJWB42KZRSV6J522O","download_json":"https://pith.science/pith/IJN7UQ36OLJWB42KZRSV6J522O.json","view_paper":"https://pith.science/paper/IJN7UQ36","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/9401206&json=true","fetch_graph":"https://pith.science/api/pith-number/IJN7UQ36OLJWB42KZRSV6J522O/graph.json","fetch_events":"https://pith.science/api/pith-number/IJN7UQ36OLJWB42KZRSV6J522O/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IJN7UQ36OLJWB42KZRSV6J522O/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IJN7UQ36OLJWB42KZRSV6J522O/action/storage_attestation","attest_author":"https://pith.science/pith/IJN7UQ36OLJWB42KZRSV6J522O/action/author_attestation","sign_citation":"https://pith.science/pith/IJN7UQ36OLJWB42KZRSV6J522O/action/citation_signature","submit_replication":"https://pith.science/pith/IJN7UQ36OLJWB42KZRSV6J522O/action/replication_record"}},"created_at":"2026-05-18T01:05:51.727896+00:00","updated_at":"2026-05-18T01:05:51.727896+00:00"}