38 citations · 84 across the 16 of their papers we have counts for
21 papers · 1 filter
The Ball-Covering Property in Lipschitz-Free Spaces
Ramón J. Aliaga, Colin Petitjean, Antonín Procházka +1
We study ball-covering properties in Lipschitz-free spaces. We establish an extension criterion for proving that fails the ball-covering property and apply it to se…
Invariant subspaces for free linearizations of Lipschitz maps
Clément Coine, Pedro L. Kaufmann, Colin Petitjean +1
We consider the invariant subspace problem for operators induced by Lipschitz self-maps on Lipschitz-free spaces. Besides the usual free linearizations of basepoint-pr…
Affine Approximation in Finite Nagata Dimension and Applications to Lipschitz-free spaces
Mingu Jung, Colin Petitjean, Antonín Prochazka +1
We show that if is a metric space of Nagata dimension at most , then there exists an atlas on modeled on such that every Lipschitz map (with val…
On Weak Compactness and Uniform Regularity in Lipschitz free Spaces
Ramón J. Aliaga, Colin Petitjean, Antonín Prochazka +1
We analyze the properties of weakly compact sets in Lipschitz free spaces. Prior research has established that, for a complete metric space , weakly precompact sets in the Lipsc…
On curve-flat Lipschitz functions and their linearizations
Gonzalo Flores, Mingu Jung, Gilles Lancien +3
We show that several operator ideals coincide when intersected with the class of linearizations of Lipschitz maps. In particular, we show that the linearization of a…
The set of elementary tensors is weakly closed in projective tensor products
Colin Petitjean
In this short note, we prove that the set of elementary tensors is weakly closed in the projective tensor product of two Banach spaces. As a result, we are able to answer a questio…
A note on the spectrum of Lipschitz operators and composition operators on Lipschitz spaces
Arafat Abbar, Clément Coine, Colin Petitjean
Fix a metric space and let be the Banach space of complex-valued Lipschitz functions defined on . A weighted composition operator on …
A pre-adjoint approach on weighted composition operators between spaces of Lipschitz functions
Arafat Abbar, Clément Coine, Colin Petitjean
We consider weighted composition operators, that is operators of the type , acting on spaces of Lipschitz functions. Bounded weighted composition opera…
Injectivity of Lipschitz operators
Luis García-Lirola, Colin Petitjean, Antonin Prochazka
Any Lipschitz map between metric spaces can be "linearised" in such a way that it becomes a bounded linear operator $\widehat{f}\colon \mathcal F(M) \to \mathcal…
Compact and weakly compact Lipschitz operators
Arafat Abbar, Clément Coine, Colin Petitjean
Any Lipschitz map between two pointed metric spaces may be extended in a unique way to a bounded linear operator betwe…
On the dynamics of Lipschitz operators
Arafat Abbar, Clément Coine, Colin Petitjean
By the linearization property of Lipschitz-free spaces, any Lipschitz map between two pointed metric spaces may be extended uniquely to a bounded linear operator $\wi…
On the Weak Maximizing Properties
Luis C. Garcia-Lirola, Colin Petitjean
Quite recently, a new property related to norm-attaining operators has been introduced: the weak maximizing property (WMP). In this note, we define a generalised version of it cons…
Compact reduction in Lipschitz free spaces
Ramón J. Aliaga, Camille Noûs, Colin Petitjean +1
We prove a general principle satisfied by weakly precompact sets of Lipschitz-free spaces. By this principle, certain infinite dimensional phenomena in Lipschitz-free spaces over g…
Embeddings of Lipschitz-free spaces into
Ramón J. Aliaga, Colin Petitjean, Antonín Procházka
We show that, for a separable and complete metric space , the Lipschitz-free space embeds linearly and almost-isometrically into if and only if is a…
On Kalton's interlaced graphs and nonlinear embeddings into dual Banach spaces
Bruno de Mendonça Braga, Gilles Lancien, Colin Petitjean +1
We study the nonlinear embeddability of Banach spaces and the equi-embeddability of the family of Kalton's interlaced graphs into dual spaces. Not…
Supports in Lipschitz-free spaces and applications to extremal structure
Ramón J. Aliaga, Eva Pernecká, Colin Petitjean +1
We show that the class of Lipschitz-free spaces over closed subsets of any complete metric space is closed under arbitrary intersections, improving upon the previously known fi…
On exposed points of Lipschitz free spaces
Colin Petitjean, Antonín Procházka
In this note we prove that a molecule is an exposed point of the unit ball of a Lispchitz free space if and only if the metric segment $[x,…
On the coarse geometry of James spaces
Gilles Lancien, Colin Petitjean, Antonín Procházka
In this note we prove that the Kalton interlaced graphs do not equi-coarsely embed into the James space nor into its dual . It is a particular case of a…
Extremal structure and Duality of Lipschitz free spaces
Luis García-Lirola, Colin Petitjean, Antonin Procházka +1
We analyse the relationship between different extremal notions in Lipschitz free spaces (strongly exposed, exposed, preserved extreme and extreme points). We prove in particular th…
On the structure of spaces of vector-valued Lipschitz functions
Luis García-Lirola, Colin Petitjean, Abraham Rueda Zoca
We analyse the strong connections between spaces of vector-valued Lipschitz functions and spaces of linear continuous operators. We apply these links to study duality, Schur proper…
Lipschitz-free spaces and Schur properties
Colin Petitjean
In this paper we study -like properties for some Lipschitz-free spaces. The main result states that, under some natural conditions, the Lipschitz-free space over a proper m…