@misc{10481/103462,
year = {2023},
month = {10},
url = {https://hdl.handle.net/10481/103462},
abstract = {Let M be a metric space and X be a Banach space. In this
paper we address several questions about the structure of F(M )̂ ⊗π X
and Lip0(M, X). Our results are the following:
(1) We prove that if M is a length metric space then Lip0(M, X)
has the Daugavet property. As a consequence, if M is length we
obtain that F(M )̂ ⊗π X has the Daugavet property. This gives an
affirmative answer to [13, Question 1] (also asked in [24, Remark
3.8]).
(2) We prove that if M is a non-uniformly discrete metric space or an
unbounded metric space then the norm of F(M )̂ ⊗π X is octahe-
dral, which solves [6, Question 3.2 (1)].
(3) We characterise all the Banach spaces X such that L(X, Y ) is
octahedral for every Banach space Y , which solves a question by
Johann Langemets.},
organization = {MCIN/AEI/10.13039/501100011033  PID2021-122126NB-C31},
organization = {Junta de Andalucía  FQM-0185, PY20_00255},
organization = {FPU19/04085 MIU (Spain)},
organization = {Czech Republic GA23-04776S, SGS22/053/OHK3/1T/13},
organization = {Fundación Séneca: ACyT Región de Murcia grant 21955/PI/22},
organization = {Generalitat Valenciana CIGE/2022/97},
publisher = {Elsevier},
keywords = {Lipschitz-free space},
keywords = {Tensor product},
keywords = {Daugavet property},
keywords = {Octahedral norms},
keywords = {Perturbation of Lipschitz maps},
title = {A characterisation of the Daugavet property in spaces of vector-valued Lipschitz functions},
doi = {10.1016/j.jfa.2025.110896},
doi = {10.48550/arXiv.2305.05956},
author = {Medina Sabino, Rubén and Rueda Zoca, Abraham},
}