Extremal Structure of Projective Tensor Products

García-Lirola, Luis C. (Universidad de Zaragoza) ; Grelier, Guillaume ; Martínez-Cervantes, Gonzalo ; Rueda Zoca, Abraham

Resumen: 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 .

Idioma: Inglés

DOI: 10.1007/s00025-023-01970-y

Año: 2023

Publicado en: Results in Mathematics 78 (2023), 196 [16 pp.]
ISSN: 1422-6383

Factor impacto JCR: 1.1 (2023)

Categ. JCR: MATHEMATICS rank: 98 / 490 = 0.2 (2023) - Q1 - T1
Categ. JCR: MATHEMATICS, APPLIED rank: 163 / 332 = 0.491 (2023) - Q2 - T2

Factor impacto CITESCORE: 1.9 - Mathematics (miscellaneous) (Q2) - Applied Mathematics (Q3)

Factor impacto SCIMAGO: 0.618 - Mathematics (miscellaneous) (Q2) - Applied Mathematics (Q2)

Financiación: info:eu-repo/grantAgreement/ES/DGA/E48-23R
Financiación: info:eu-repo/grantAgreement/ES/MICINN-AEI-FEDER/PID2021-122126NB-C31
Financiación: info:eu-repo/grantAgreement/ES/MICINN-AEI-FEDER/PID2021-122126NB-C32

Tipo y forma: Article (Published version)

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