{"paper":{"title":"$L_p +L_q$ and $L_p \\cap L_q$ are not isomorphic for all $1 \\leq p, q \\leq \\infty$, $p \\neq q$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Lech Maligranda, Sergey Astashkin","submitted_at":"2018-04-10T12:04:21Z","abstract_excerpt":"We prove that if $1 \\leq p, q \\leq \\infty$, then the spaces $L_p +L_q$ and $L_p \\cap L_q$ are isomorphic if and only if $p = q$. In particular, $L_2 +L_{\\infty}$ and $L_2 \\cap L_{\\infty}$ are not isomorphic which is an answer to a question formulated in the paper S. V. Astashkin and L. Maligranda, \\textit{$L_p + L_{\\infty}$ and $L_p \\cap L_{\\infty}$ are not isomorphic for all $1 \\leq p < \\infty, p \\neq 2$}, Proc. Amer. Math. Soc. 146 (2018), no. 5, 2181--2194."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03469","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"}