{"paper":{"title":"The Bishop-Phelps-Bollob\\'{a}s theorem for operators on $L_1(\\mu)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Han Ju Lee, Miguel Mart\\'in, Sun Kwang Kim, Yun Sung Choi","submitted_at":"2013-03-25T10:45:42Z","abstract_excerpt":"In this paper we show that the Bishop-Phelps-Bollob\\'as theorem holds for $\\mathcal{L}(L_1(\\mu), L_1(\\nu))$ for all measures $\\mu$ and $\\nu$ and also holds for $\\mathcal{L}(L_1(\\mu),L_\\infty(\\nu))$ for every arbitrary measure $\\mu$ and every localizable measure $\\nu$. Finally, we show that the Bishop-Phelps-Bollob\\'as theorem holds for two classes of bounded linear operators from a real $L_1(\\mu)$ into a real $C(K)$ if $\\mu$ is a finite measure and $K$ is a compact Hausdorff space. In particular, one of the classes includes all Bochner representable operators and all weakly compact operators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.6078","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"}