Extremal structure in ultrapowers of Banach spaces

García-Lirola, L. C. (Universidad de Zaragoza) ; Grelier, G. ; Rueda Zoca, A.

Resumen: 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).

Idioma: Inglés

DOI: 10.1007/s13398-022-01311-8

Año: 2022

Publicado en: Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas 116, 4 (2022), 161 [25 pp]
ISSN: 1578-7303

Factor impacto JCR: 2.9 (2022)

Categ. JCR: MATHEMATICS rank: 15 / 329 = 0.046 (2022) - Q1 - T1

Factor impacto CITESCORE: 4.9 - Mathematics (Q1)

Factor impacto SCIMAGO: 0.933 - Algebra and Number Theory (Q1) - Analysis (Q1) - Geometry and Topology (Q1) - Computational Mathematics (Q1) - Applied Mathematics (Q1)

Financiación: info:eu-repo/grantAgreement/ES/AEI-FEDER/ MTM2017-83262-C2-2-P

Tipo y forma: Artículo (Versión definitiva)

Área (Departamento): Área Análisis Matemático (Dpto. Matemáticas)