Zobrazeno 1 - 10
of 60
pro vyhledávání: '"Aliaga, Ramón J."'
Let $\mathrm{Lip}_0(M)$ be the space of Lipschitz functions on a complete metric space $(M,d)$ that vanish at a point $0\in M$. We investigate its dual $\mathrm{Lip}_0(M)^*$ using the de Leeuw transform, which allows representing each functional on $
Externí odkaz:
http://arxiv.org/abs/2403.09546
We prove that several classical Banach space properties are equivalent to separability for the class of Lipschitz-free spaces, including Corson's property ($\mathcal{C}$), Talponen's Countable Separation Property, or being a G\^ateaux differentiabili
Externí odkaz:
http://arxiv.org/abs/2312.14678
Autor:
Abrahamsen, Trond A., Aliaga, Ramón J., Lima, Vegard, Martiny, André, Perreau, Yoël, Prochazka, Antonín, Veeorg, Triinu
We introduce relative versions of Daugavet-points and the Daugavet property, where the Daugavet-behavior is localized inside of some supporting slice. These points present striking similarities with Daugavet-points, but lie strictly between the notio
Externí odkaz:
http://arxiv.org/abs/2306.05536
Autor:
Abrahamsen, Trond A., Aliaga, Ramón J., Lima, Vegard, Martiny, André, Perreau, Yoël, Prochazka, Antonín, Veeorg, Triinu
Publikováno v:
J. London Math. Soc. 109 (2024), e12913
We show that the Lipschitz-free space with the Radon--Nikod\'{y}m property and a Daugavet point recently constructed by Veeorg is in fact a dual space isomorphic to $\ell_1$. Furthermore, we answer an open problem from the literature by showing that
Externí odkaz:
http://arxiv.org/abs/2303.00511
Publikováno v:
Journal of Functional Analysis 287 (2024), 110560
We introduce convex integrals of molecules in Lipschitz-free spaces $\mathcal{F}(M)$ as a continuous counterpart of convex series considered elsewhere, based on the de Leeuw representation. Using optimal transport theory, we show that these elements
Externí odkaz:
http://arxiv.org/abs/2302.13951
Publikováno v:
In Journal of Functional Analysis 15 October 2024 287(8)
Publikováno v:
Trans. Amer. Math. Soc. 375 (2022), no. 5, pp. 3529-3567
We characterize compact metric spaces whose locally flat Lipschitz functions separate points uniformly as exactly those that are purely 1-unrectifiable, resolving a problem of Weaver. We subsequently use this geometric characterization to answer seve
Externí odkaz:
http://arxiv.org/abs/2103.09370
Autor:
Aliaga, Ramón J.
Publikováno v:
Mediterr. J. Math. 19 (2022), art. 32
We prove that all extreme points of the unit ball of a Lipschitz-free space over a compact metric space have finite support. Combined with previous results, this completely characterizes extreme points and implies that all of them are also extreme po
Externí odkaz:
http://arxiv.org/abs/2102.01219
Autor:
Aliaga, Ramón J., Pernecká, Eva
Publikováno v:
Int. Math. Res. Not. (2021), available online
We analyze the relationship between Borel measures and continuous linear functionals on the space $\mathrm{Lip}_0(M)$ of Lipschitz functions on a complete metric space $M$. In particular, we describe continuous functionals arising from measures and v
Externí odkaz:
http://arxiv.org/abs/2009.07663
Autor:
Aliaga, Ramón J., Pernecká, Eva
Publikováno v:
J. Inst. Math. Jussieu 21 (2022), pp. 2093-2102
Let $\operatorname{Lip}_0(M)$ be the space of Lipschitz functions on a complete metric space $M$ that vanish at a base point. We show that every normal functional in $\operatorname{Lip}_0(M)^\ast$ is weak$^*$ continuous, answering a question by N. We
Externí odkaz:
http://arxiv.org/abs/2004.14310