{"paper":{"title":"Geometric implications of the M(r,s)-properties and the uniform Kadec-Klee property in JB*-triples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Antonio M. Peralta, Eduardo Nieto, Lei Li","submitted_at":"2016-04-14T11:50:20Z","abstract_excerpt":"We explore new implications of the $M(r,s)$ and $M^*(r,s)$ properties for Banach spaces. We show that a Banach space $X$ satisfying property $M(1,s)$ for some $0<s\\leq 1$, admitting a point $x_{0}$ in its unit sphere at which the relative weak and norm topologies agree, satisfies the generalized Gossez-Lami Dozo property. We establish sufficient conditions, in terms of the $(r, s)$-Lipschitz weak$^*$ Kadec-Klee property on a Banach space $X$, to guarantee that its dual space satisfies the UKK$^*$ property. We determine appropriate conditions to assure that a Banach space $X$ satisfies the $(r,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.04119","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"}