@misc{10481/102416,
year = {2024},
url = {https://hdl.handle.net/10481/102416},
abstract = {We construct a Banach space X for which the set of norm-attaining functionals
NA(X, R) does not contain any non-trivial cone. Even more, given two linearly independent
norm-attaining functionals on X, no other element of the segment between them attains its
norm. Equivalently, the intersection of NA(X, R) with a two-dimensional subspace of X∗ is
contained in the union of two lines. In terms of proximinality, we show that for every closed
subspace M of X of codimension two, at most four elements of the unit sphere of X/M have
a representative of norm-one. We further relate this example with an open problem on normattaining operators.},
organization = {MICIU/AEI/10.13039/501100011033 PID2021-122126NB-C31},
organization = {ERDF/EU},
organization = {MICIU/AEI/10.13039/501100011033 Maria de Maeztu CEX2020-001105-M},
publisher = {Elsevier},
title = {A Banach space whose set of norm-attaining functionals is algebraically trivial},
doi = {10.1016/j.jfa.2024.110815},
author = {Martín Suárez, Miguel},
}