{"paper":{"title":"Subspaces of maximal dimension contained in $L_p(\\Omega) - \\bigcup\\limits_{q<p} L_q (\\Omega)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"D. Cariello, D. Pellegrino, G. Botelho, J.B. Seoane-Sep\\'ulveda, V.V. F\\'avaro","submitted_at":"2012-04-10T14:50:28Z","abstract_excerpt":"Let $(\\Omega,\\Sigma,\\mu)$ be a measure space and $1< p < +\\infty$. In this paper we show that, under quite general conditions, the set $L_{p}(\\Omega) - \\bigcup\\limits_{1 \\leq q < p}L_{q}(\\Omega)$ is maximal spaceable, that is, it contains (except for the null vector) a closed subspace $F$ of $L_{p}(\\Omega)$ such that $\\dim(F) = \\dim(L_{p}(\\Omega))$. We also show that if those conditions are not fulfilled, then even the larger set $L_p(\\Omega) - L_q(\\Omega)$, $1 \\leq q < p$, may fail to be maximal spaceable. The aim of the results presented here is, among others, to generalize all the previous "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2170","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"}