@misc{10481/84240,
year = {2023},
month = {7},
url = {https://hdl.handle.net/10481/84240},
abstract = {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
 ⊗πY 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
 ⊗πY (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  2 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
 ⊗πX.},
organization = {Agencia Estatal de Investigación},
organization = {EDRF/FEDER "A way of making Europe" (MCIN/AEI)	PID2021-122126NB-C32
PID2021-122126NB-C31},
organization = {Fundacion Seneca	21955/PI/22},
organization = {DGA project	E48-23R},
organization = {MICINN 2018 FPI fellowship	PRE2018-083703},
publisher = {Springer Nature},
keywords = {Banach space},
keywords = {Projective tensor product},
keywords = {Preserved extreme point},
keywords = {Strongly exposed point},
title = {Extremal Structure of Projective Tensor Products},
doi = {10.1007/s00025-023-01970-y},
author = {García Lirola, Luis and Rueda Zoca, Abraham},
}