118799 20240319081003.0 doi 10.1007/s13398-022-01311-8 sideral 129985 ART-2022-129985 eng García-Lirola, L. C. Universidad de Zaragoza (orcid)0000-0001-9211-4475 Extremal structure in ultrapowers of Banach spaces 2022 Access copy available to the general public Unrestricted Given a bounded convex subset C of a Banach space X and a free ultrafilter U, we study which points (xi)U are extreme points of the ultrapower CU in XU. In general, we obtain that when { xi} is made of extreme points (respectively denting points, strongly exposed points) and they satisfy some kind of uniformity, then (xi)U is an extreme point (respectively denting point, strongly exposed point) of CU. We also show that every extreme point of CU is strongly extreme, and that every point exposed by a functional in (X*)U is strongly exposed, provided that U is a countably incomplete ultrafilter. Finally, we analyse the extremal structure of CU in the case that C is a super weakly compact or uniformly convex set. © 2022, The Author(s). info:eu-repo/grantAgreement/ES/AEI-FEDER/ MTM2017-83262-C2-2-P info:eu-repo/semantics/openAccess by http://creativecommons.org/licenses/by/3.0/es/ 2.9 2022 MATHEMATICS 15 / 329 = 0.046 2022 Q1 T1 0.933 2022 Algebra and Number Theory 2022 Q1 Analysis 2022 Q1 Geometry and Topology 2022 Q1 Computational Mathematics 2022 Q1 Applied Mathematics 2022 Q1 4.9 2022 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Grelier, G. Rueda Zoca, A. 2006 015 Universidad de Zaragoza Dpto. Matemáticas Área Análisis Matemático 116, 4 (2022), 161 [25 pp] Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas 1578-7303 456917 http://zaguan.unizar.es/record/118799/files/texto_completo.pdf Versión publicada 1288958 http://zaguan.unizar.es/record/118799/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:118799 articulos driver 2024-03-18-14:23:51 ARTICLE