{"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"}