{"paper":{"title":"The Bishop-Phelps-Bollob\\'as point property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Han Ju Lee, Sheldon Dantas, Sun Kwang Kim","submitted_at":"2016-05-01T12:40:57Z","abstract_excerpt":"In this article, we study a version of the Bishop-Phelps-Bollob\\'as property. We investigate a pair of Banach spaces $(X, Y)$ such that every operator from $X$ into $Y$ is approximated by operators which attains its norm at the same point where the original operator almost attains its norm. In this case, we say that such a pair has the Bishop-Phelps-Bollob\\'as point property (BPBpp). We characterize uniform smoothness in terms of BPBpp and we give some examples of pairs $(X, Y)$ which have and fail this property. Some stability results are obtained about $\\ell_1$ and $\\ell_\\infty$ sums of Bana"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00245","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"}