Embeddings of Lipschitz-free spaces into ℓ1

Autor: Antonín Procházka, Ramón J. Aliaga, Colin Petitjean

Publikováno v: Journal of Functional Analysis
Journal of Functional Analysis, Elsevier, 2021, 280 (6), pp.108916. ⟨10.1016/j.jfa.2020.108916⟩
Journal of Functional Analysis, Elsevier, 2021, 280 (6), pp.108916
RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
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[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 length measure 0. Moreover,

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::01d918de8837cbc4dee72615a465675c
https://hal.science/hal-02974707

Integral representation and supports of functionals on Lipschitz spaces

Autor: Eva Pernecká, Ramón J. Aliaga

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: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9b8c037c2e98015ba2a78bce67cb5c24
http://arxiv.org/abs/2009.07663

Compact reduction in Lipschitz-free spaces - RETRACTION

Autor: Ramón J. Aliaga, Camille Noûs, Colin Petitjean, Antonín Procházka

Publikováno v: Proceedings of the Royal Society of Edinburgh: Section A Mathematics. 151:2082-2082

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::d8b62ad7c479a70658e0bc6b4c8916d6
https://doi.org/10.1017/prm.2021.87

Supports in Lipschitz-free spaces and applications to extremal structure

Autor: Eva Pernecká, Ramón J. Aliaga, Colin Petitjean, Antonín Procházka

Publikováno v: RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
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Journal of Mathematical Analysis and Applications
Journal of Mathematical Analysis and Applications, Elsevier, 2020, 489 (1), pp.124128. ⟨10.1016/j.jmaa.2020.124128⟩

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 formulate a general and natural

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d431a839dc3fa19bde4e3f11aa255f09
https://doi.org/10.1016/j.jmaa.2020.124128

Supports and extreme points in Lipschitz-free spaces

Autor: Ramón J. Aliaga, Eva Pernecká

Publikováno v: RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
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For a complete metric space $M$, we prove that the finitely supported extreme points of the unit ball of the Lipschitz-free space $\mathcal{F}(M)$ are precisely the elementary molecules $(\delta(p)-\delta(q))/d(p,q)$ defined by pairs of points $p,q$

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a6d3e82a2e927e3636bd886fc2609d32
http://arxiv.org/abs/1810.11278