{"paper":{"title":"Banach Spaces Of The Type Of Tsirelson","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Irene Deliyanni, Spiros A. Argyros","submitted_at":"1992-07-06T16:04:20Z","abstract_excerpt":"To any pair ( M , theta ) where M is a family of finite subsets of N compact in the pointwise topology, and 0<theta < 1 , we associate a Tsirelson-type Banach space T_M^theta . It is shown that if the Cantor-Bendixson index of M is greater than n and theta >{1/n} then T_M^theta is reflexive. Moreover, if the Cantor-Bendixson index of M is greater than omega then T_M^theta does not contain any l^p, while if the Cantor-Bendixson index of M is finite thenT_M^theta contains some l^p or c_o . In particular, if M ={ A subset N : |A| leq n } and {1/n}<theta <1 then T_M^theta is isomorphic to some l^p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9207206","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"}