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Listar por palabra clave "Lipschitz-free space"

Mostrando ítems 1-10 de 10

Compact reduction in Lipschitz-free spaces

Aliaga, Ramón J.; Nous, Camille; Petitjean, Colin; Prochazka, Antonin (Institute of Mathematics, Polish Academy of Sciences, 2021)

[EN] We prove a general principle satisfied by weakly precompact sets of Lip-schitz-free spaces. By this principle, certain infinite-dimensional phenomena in Lipschitzfree spaces over general metric spaces may be reduced ...
Embeddings of Lipschitz-free spaces into l(1)

Aliaga, Ramón J.; Petitjean, Colin; Prochazka, Antonin (Elsevier, 2021-03-15)

[EN] We show that, for a separable and complete metric space $M$, the Lipschitz-free space $\mathcal{F}(M)$ embeds linearly and almost-isometrically into $\ell_1$ if and only if $M$ is a subset of an $\mathbb{R}$-tree with ...
Extreme points in Lipschitz-free spaces over compact metric spaces

Aliaga, Ramón J. (Springer-Verlag, 2022-02)

[EN] 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 ...
Geometry and structure of Lipschitz-free spaces and their biduals

Aliaga Varea, Ramón José (Universitat Politècnica de València, 2021-01-17)

[ES] Los espacios libres Lipschitz F(M) son linearizaciones canónicas de espacios métricos M cualesquiera. Más concretamente, F(M) es el único espacio de Banach que contiene una copia isométrica de M que es linearmente ...
Normal functionals on Lipschitz spaces are weak* continuous

Aliaga, Ramón J.; Pernecká, Eva (Cambridge University Press, 2022-11)

[EN] Let Lip0(M) be the space of Lipschitz functions on a complete metric space M that vanish at a base point. We prove that every normal functional in Lip0(M)¿ is weak* continuous; that is, in order to verify weak* ...
On the preserved extremal structure of Lipschitz-free spaces

Aliaga, Ramón J.; Guirao Sánchez, Antonio José (Institute of Mathematics, Polish Academy of Sciences, 2019)

[EN] 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 ...
Points of differentiability of the norm in Lipschitz-free spaces

Aliaga, Ramón J.; Rueda Zoca, Abraham (Elsevier, 2020-09-15)

[EN] We consider convex series of molecules in Lipschitz-free spaces, i.e. elements of the form such that . We characterise these elements in terms of geometric conditions on the points , of the underlying metric space, ...
Purely 1-unrectifiable metric spaces and locally flat Lipschitz functions

Aliaga, Ramón J.; Gartland, Chris; Petitjean, Colin; Procházka, Antonín (American Mathematical Society, 2022-05)

[EN] We characterize compact metric spaces whose locally flat Lip-schitz functions separate points uniformly as exactly those that are purely 1-unrectifiable, resolving a problem of Weaver. We subsequently use this geometric ...
Supports and extreme points in Lipschitz-free spaces

Aliaga, Ramón J.; Pernecka, Eva (European Mathematical Society Publishing House, 2020)

[EN] For a complete metric space M, we prove that the finitely supported extreme points of the unit ball of the Lipschitz-free space F(M) are precisely the elementary molecules (¿(p)¿¿(q))/d(p,q) defined by pairs of points ...
Supports in Lipschitz-free spaces and applications to extremal structure

Aliaga, Ramón J.; Pernecká, Eva; Petitjean, Colin; Procházka, Antonín (Elsevier, 2020-09-01)

[EN] We show that the class of Lipschitz-free spaces over closed subsets of any complete metric space M is closed under arbitrary intersections, improving upon the previously known finite-diameter case. This allows us to ...