{"paper":{"title":"On asymptotic properties of Banach spaces under renormings","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Edward Odell, Thomas Schlumprecht","submitted_at":"1997-09-18T00:00:00Z","abstract_excerpt":"It is shown that a separable Banach space $X$ can be given an equivalent norm $|\\!|\\!|\\cdot |\\!|\\!|$ with the following properties:\\quad If $(x_n)\\subseteq X$ is relatively weakly compact and $\\lim_{m\\to\\infty} \\lim_{n\\to\\infty}\\break |\\!|\\!| x_m + x_n |\\!|\\!| = 2\\lim_{m\\to\\infty} |\\!|\\!| x_m|\\!|\\!|$ then $(x_n)$ converges in norm. This yields a characterization of reflexivity once proposed by V.D.~Milman. In addition it is shown that some spreading model of a sequence in $(X, |\\!|\\!|\\cdot |\\!|\\!|)$ is 1-equivalent to the unit vector basis of $\\ell_1$ (respectively, $c_0$) implies that $X$ con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9709217","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"}