{"paper":{"title":"There is no operatorwise version of the Bishop-Phelps-Bollob\\'as property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Han Ju Lee, Miguel Mart\\'in, Sheldon Dantas, Sun Kwang Kim, Vladimir Kadets","submitted_at":"2018-10-01T14:30:01Z","abstract_excerpt":"Given two real Banach spaces $X$ and $Y$ with dimensions greater than one, it is shown that there is a sequence $\\{T_n\\}_{n\\in \\mathbb{N}}$ of norm attaining norm-one operators from $X$ to $Y$ and a point $x_0\\in X$ with $\\|x_0\\|=1$, such that $\\|T_n(x_0)\\|\\longrightarrow 1$ but $\\inf_{n \\in \\mathbb{N}} \\{\\mbox{dist} (x_0,\\,\\{x\\in X: \\|T_n(x)\\|=\\|x\\|=1\\})\\} >0.$ This shows that a version of the Bishop-Phelps-Bollob\\'as property in which the operator is not changed is possible only if one of the involved Banach spaces is one-dimensional."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00684","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"}