@misc{10481/98293,
year = {2020},
url = {https://hdl.handle.net/10481/98293},
abstract = {We prove that the abundance of almost L-orthogonal vectors
in a Banach space X (almost Daugavet property) implies the abundance
of nonzero vectors in X** being L-orthogonal to X. In fact, we
get that a Banach space X verfies the Daugavet property if, and only
if, the set of vectors in X** being L-orthogonal to X is weak-star dense
in X**. In contrast with the separable case, we prove that the existence
of almost L-orthogonal vectors in a nonseparable Banach space
X (octahedrality) does not imply the existence of nonzero vectors in
X** being L-orthogonal to X, which shows that the answer to an environment
question is negative (see [7, Section 9] and [13, Section 4]).
Also, in contrast with the separable case, we obtain that the existence of
almost L-orthogonal vectors in a nonseparable Banach space X (octahedrality)
does not imply the abundance of almost L-orthogonal vectors
in Banach space X (almost Daugavet property), which solves an open
question in [20]. Some consequences on Daugavet property in the setting
of L-embedded spaces are also obtained.},
organization = {MICINN (Spain) Grant PGC2018- 093794-B-I00 (MCIU, AEI, FEDER, UE),},
organization = {Junta de Andalucía Grant A-FQM-484- UGR18},
organization = {Junta de Andalucía Grant FQM-0185},
organization = {Vicerrectorado de Investigación y Transferencia de la Universidad de Granada in the program \Contratos puente},
title = {L- Orthogonality, octahedrality and daugavet property in banach spaces},
author = {López Pérez, Ginés and Rueda, Abraham},
}