TY  - JOUR
AU  - Aliaga, R. J.
AU  - Guirao, A. J.
PY  - 2019
DA  - 2019//
TI  - On the preserved extremal structure of Lipschitz-free spaces
T2  - Studia Math.
JO  - Studia Mathematica
SP  - 1
EP  - 14
VL  - 245
IS  - 1
PB  - Polish Acad Sciences Inst Mathematics-Impan
KW  - concave space
KW  - extremal structure
KW  - Lipschitz-free space
KW  - Lipschitz function
KW  - metric alignment
KW  - preserved extreme point
AB  - We characterize preserved extreme points of the unit ball of Lipschitz-free spaces F (X) in terms of simple geometric conditions on the underlying metric space (X, d). Namely, the preserved extreme points are the elementary molecules corresponding to pairs of points p, q in X such that the triangle inequality d (p, q) <= d (p, r) + d (q, r) is uniformly strict for r away from p, q. For compact X, this condition reduces to the triangle inequality being strict. As a consequence, we give an affirmative answer to a conjecture of N. Weaver that compact spaces are concave if and only if they have no triple of metrically aligned points, and we show that all extreme points are preserved for several classes of compact metric spaces X, including Holder and countable compacta.
SN  - 0039-3223
UR  - http://arxiv.org/abs/1705.09579
UR  - https://doi.org/10.4064/sm170529-30-11
DO  - 10.4064/sm170529-30-11
LA  - English
N1  - WOS:000446980500001
ID  - Aliaga+Guirao2019
ER  -