000127915 001__ 127915 000127915 005__ 20241125101144.0 000127915 0247_ $$2doi$$a10.1007/s00025-023-01970-y 000127915 0248_ $$2sideral$$a135020 000127915 037__ $$aART-2023-135020 000127915 041__ $$aeng 000127915 100__ $$0(orcid)0000-0001-9211-4475$$aGarcía-Lirola, Luis C.$$uUniversidad de Zaragoza 000127915 245__ $$aExtremal Structure of Projective Tensor Products 000127915 260__ $$c2023 000127915 5060_ $$aAccess copy available to the general public$$fUnrestricted 000127915 5203_ $$aWe 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 . 000127915 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E48-23R$$9info:eu-repo/grantAgreement/ES/MICINN-AEI-FEDER/PID2021-122126NB-C31$$9info:eu-repo/grantAgreement/ES/MICINN-AEI-FEDER/PID2021-122126NB-C32 000127915 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/ 000127915 590__ $$a1.1$$b2023 000127915 592__ $$a0.618$$b2023 000127915 591__ $$aMATHEMATICS$$b98 / 490 = 0.2$$c2023$$dQ1$$eT1 000127915 593__ $$aMathematics (miscellaneous)$$c2023$$dQ2 000127915 591__ $$aMATHEMATICS, APPLIED$$b163 / 332 = 0.491$$c2023$$dQ2$$eT2 000127915 593__ $$aApplied Mathematics$$c2023$$dQ2 000127915 594__ $$a1.9$$b2023 000127915 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000127915 700__ $$aGrelier, Guillaume 000127915 700__ $$aMartínez-Cervantes, Gonzalo 000127915 700__ $$aRueda Zoca, Abraham 000127915 7102_ $$12006$$2015$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Análisis Matemático 000127915 773__ $$g78 (2023), 196 [16 pp.]$$pResults in Mathematics$$tResults in Mathematics$$x1422-6383 000127915 8564_ $$s400645$$uhttps://zaguan.unizar.es/record/127915/files/texto_completo.pdf$$yVersión publicada 000127915 8564_ $$s1076628$$uhttps://zaguan.unizar.es/record/127915/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000127915 909CO $$ooai:zaguan.unizar.es:127915$$particulos$$pdriver 000127915 951__ $$a2024-11-22-12:03:39 000127915 980__ $$aARTICLE