127915 20241125101144.0 doi 10.1007/s00025-023-01970-y sideral 135020 ART-2023-135020 eng García-Lirola, Luis C. Universidad de Zaragoza (orcid)0000-0001-9211-4475 Extremal Structure of Projective Tensor Products 2023 Access copy available to the general public Unrestricted We prove that, given two Banach spaces X and Y and bounded, closed convex sets C⊆X and D⊆Y , if a nonzero element z∈co¯¯¯¯¯¯(C⊗D)⊆X⊗ˆπY is a preserved extreme point then z=x0⊗y0 for some preserved extreme points x0∈C and y0∈D , whenever K(X,Y∗) separates points of X⊗ˆπY (in particular, whenever X or Y has the compact approximation property). Moreover, we prove that if x0∈C and y0∈D are weak-strongly exposed points then x0⊗y0 is weak-strongly exposed in co¯¯¯¯¯¯(C⊗D) whenever x0⊗y0 has a neighbourhood system for the weak topology defined by compact operators. Furthermore, we find a Banach space X isomorphic to ℓ2 with a weak-strongly exposed point x0∈BX such that x0⊗x0 is not a weak-strongly exposed point of the unit ball of X⊗ˆπX . info:eu-repo/grantAgreement/ES/DGA/E48-23R info:eu-repo/grantAgreement/ES/MICINN-AEI-FEDER/PID2021-122126NB-C31 info:eu-repo/grantAgreement/ES/MICINN-AEI-FEDER/PID2021-122126NB-C32 info:eu-repo/semantics/openAccess by http://creativecommons.org/licenses/by/3.0/es/ 1.1 2023 MATHEMATICS 98 / 490 = 0.2 2023 Q1 T1 MATHEMATICS, APPLIED 163 / 332 = 0.491 2023 Q2 T2 0.618 2023 Mathematics (miscellaneous) 2023 Q2 Applied Mathematics 2023 Q2 1.9 2023 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Grelier, Guillaume Martínez-Cervantes, Gonzalo Rueda Zoca, Abraham 2006 015 Universidad de Zaragoza Dpto. Matemáticas Área Análisis Matemático 78 (2023), 196 [16 pp.] Results in Mathematics Results in Mathematics 1422-6383 400645 http://zaguan.unizar.es/record/127915/files/texto_completo.pdf Versión publicada 1076628 http://zaguan.unizar.es/record/127915/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:127915 articulos driver 2024-11-22-12:03:39 ARTICLE