{"paper":{"title":"Ordinal Indices of small subspaces of $L_p$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"D. Khurana, S. Dutta","submitted_at":"2014-09-08T13:11:04Z","abstract_excerpt":"We calculate ordinal $L_p$ index defined in \"An ordinal L_p index for Banach spaces with an application to complemented subspaces of L_p\" authored by J. Bourgain, H. P. Rosenthal and G. Schechtman, for Rosenthal's space $X_p$, $\\ell_p$ and $\\ell_2$. We show a subspace of $L_p$ $(2 < p < \\infty)$ non isomorphic to $\\ell_2$ embeds in $\\ell_p$ if and only if its ordinal index is minimum possible. We also give a sufficient condition for a $\\mathcal{L}_p$ subspace of $\\ell_p\\oplus\\ell_2$ to be isomorphic to $X_p$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.2330","kind":"arxiv","version":2},"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"}