{"paper":{"title":"Two refinements of the Bishop-Phelps-Bollob\\'as modulus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Javier Meri, Mariia Soloviova, Mario Chica, Miguel Martin, Vladimir Kadets","submitted_at":"2014-10-21T08:18:09Z","abstract_excerpt":"Extending the celebrated result by Bishop and Phelps that the set of norm attaining functionals is always dense in the topological dual of a Banach space, Bollob\\'as proved the nowadays known as the Bishop-Phelps-Bollob\\'as theorem, which allows to approximate at the same time a functional and a vector in which it almost attains the norm. Very recently, two Bishop-Phelps-Bollob\\'as moduli of a Banach space have been introduced [J. Math. Anal. Appl. 412 (2014), 697--719] to measure, for a given Banach space, what is the best possible Bishop-Phelps-Bollob\\'as theorem in this space. In this paper"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5570","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"}