{"paper":{"title":"On the geometry of higher order Schreier spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Hung Viet Chu, Kevin Beanland, Leandro Antunes","submitted_at":"2019-03-08T15:21:44Z","abstract_excerpt":"For each countable ordinal $\\alpha$ let $\\mathcal{S}_{\\alpha}$ be the Schreier set of order $\\alpha$ and $X_{\\mathcal{S}_\\alpha}$ be the corresponding Schreier space of order $\\alpha$. In this paper we prove several new properties of these spaces. 1) If $\\alpha$ is non-zero then $X_{\\mathcal{S}_\\alpha}$ possesses the $\\lambda$-property of R. Aron and R. Lohman and is a $(V)$-polyhedral spaces in the sense on V. Fonf and L. Vesely. 2) If $\\alpha$ is non-zero and $1<p<\\infty$ then the $p$-convexification $X^{p}_{\\mathcal{S}_\\alpha}$ possesses the uniform $\\lambda$-property of R. Aron and R. Lohm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.03492","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"}