{"paper":{"title":"The Szlenk Index of L_p(X)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Petr Hajek, Thomas Schlumprecht","submitted_at":"2013-08-16T13:51:07Z","abstract_excerpt":"We find an optimal upper bound on the values of the weak$^*$-dentability index $Dz(X)$ in terms of the Szlenk index $Sz(X)$ of a Banach space $X$ with separable dual. Namely, if $\\;Sz(X)=\\omega^{\\alpha}$, for some $\\alpha<\\omega_1$, and $p\\in(1,\\infty)$, then\n  $$Sz(X)\\le Dz(X)\\le Sz(L_p(X))\\le {cases} \\omega^{\\alpha+1} &\\text{if $\\alpha$ is a finite ordinal,}\n  \\omega^{\\alpha} &\\text{if $\\alpha$ is an infinite ordinal.}\n  {cases}$$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.3629","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"}