Results 11 to 20 of about 55,940 (168)
Weakly almost square Lipschitz-free spaces
Journal of Mathematical Analysis and Applications, 2023 We construct a Lipschitz-free space that is locally almost square but not weakly almost square; this is the first example of such a Banach space. We also prove a result, which indicates that geodesic metric spaces are a potential metric characterization for weakly almost square Lipschitz-free spaces. Lastly, we prove that a Lipschitz-free space can not
Jaan Kristjan Kaasik, Triinu Veeorg
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On the structure of Lipschitz-free spaces [PDF]
Proceedings of the American Mathematical Society, 2016 In this note we study the structure of Lipschitz-free Banach spaces. We show that every Lipschitz-free Banach space over an infinite metric space contains a complemented copy of ℓ 1 \ell _1 . This result has many consequences for the structure of Lipschitz-free Banach spaces.
Cúth, Marek +2 more
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Extreme Points in Lipschitz-Free Spaces over Compact Metric Spaces [PDF]
Mediterranean Journal of Mathematics, 2022 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 points in the bidual ball.
Ramón J Aliaga
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Tree metrics and their Lipschitz-free spaces [PDF]
Proceedings of the American Mathematical Society, 2010 We compute the Lipschitz-free spaces of subsets of the real line and characterize subsets of metric trees by the fact that their Lipschitz-free space is isometric to a subspace of L 1 L_1 .
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Lipschitz-free spaces and Schur properties
Journal of Mathematical Analysis and Applications, 2017 In this paper we study $\ell_1$-like properties for some Lipschitz-free spaces. The main result states that, under some natural conditions, the Lipschitz-free space over a proper metric space linearly embeds into an $\ell_1$-sum of finite dimensional subspaces of itself.
Colin Petitjean
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On Schauder bases in Lipschitz-free spaces
Journal of Mathematical Analysis and Applications, 2014 For a pointed metric space \(M\), consider the Banach space \(\mathrm{Lip}_0(M)\) of Lipschitz real-valued functions on \(M\) vanishing at \(0\), endowed with the norm defined by the Lipschitz constant. Its unit ball being compact for the pointwise convergence topology, this space is a dual space and a canonical predual of \(\mathrm{Lip}_0(M)\) is ...
Hájek, P. (Petr Pavel) +1 more
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Octahedrality in Lipschitz-free Banach spaces [PDF]
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2017 The aim of this note is to study octahedrality in vector-valued Lipschitz-free Banach spaces on a metric space, under topological hypotheses on it, by analysing the weak-star strong diameter 2 property in Lipschitz function spaces. Also, we show an example that proves that our results are optimal and that octahedrality in vector-valued Lipschitz-free ...
Guerrero, Julio Becerra +2 more
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Lipschitz free spaces over locally compact metric spaces [PDF]
Studia Mathematica, 2021 27 pages. Changes to names of some objects and addition of informal discussion of semi-embedding theorem.
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Approximation properties in Lipschitz‐free spaces over groups [PDF]
Journal of the London Mathematical Society, 2022 With updated ...
Doucha, Michal +1 more
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On some Banach space constants arising in nonlinear fixed point and eigenvalue theory
Fixed Point Theory and Applications, 2004 As is well known, in any infinite-dimensional Banach space one may find fixed point free self-maps of the unit ball, retractions of the unit ball onto its boundary, contractions of the unit sphere, and nonzero maps without positive eigenvalues and ...
Martin Väth +3 more
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