10 papers · 1 filter
Extremal structure in ultrapowers of Banach spaces
Luis C. García-Lirola, Guillaume Grelier, Abraham Rueda Zoca
Given a bounded convex subset of a Banach space and a free ultrafilter , we study which points are extreme points of the ultrapower $C_\mathc…
On norm-attainment in (symmetric) tensor products
Sheldon Dantas, Luis C. García-Lirola, Mingu Jung +1
In this paper, we introduce a concept of norm-attainment in the projective symmetric tensor product of a Banach space , which turns out to be natur…
Uniformly convex renormings and generalized cotypes
Luis C. García-Lirola, Matías Raja
We are concerned about improvements of the modulus of convexity by renormings of a super-reflexive Banach space. Typically optimal results are beyond Pisier's power functions bound…
Examples and applications of the density of strongly norm attaining Lipschitz maps
Rafael Chiclana, Luis C. García-Lirola, Miguel Martin +1
We study the density of the set of those Lipschitz maps from a (complete pointed) metric space to a Banach space which strongly attain their norm…
Pełczyński space is isomorphic to the Lipschitz free space over a compact set
Luis C. García-Lirola, Antonin Prochazka
We prove the result stated in the title. This provides a first example of an infinite-dimensional Banach space whose Lipschitz free space is isomorphic to the free space of a compa…
A characterisation of the Daugavet property in spaces of Lipschitz functions
Luis García-Lirola, Antonín Procházka, Abraham Rueda Zoca
We study the Daugavet property in the space of Lipschitz functions for a complete metric space . Namely we show that has the…
Maps with the Radon-Nikodým property
Luis García-Lirola, Matías Raja
We study dentable maps from a closed convex subset of a Banach space into a metric space as an attempt of generalize the Radon-Nikodým property to a "less linear" frame. We note 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…
Unconditional almost squareness and applications to spaces of Lipschitz functions
Luis García-Lirola, Abraham Rueda Zoca
We introduce an unconditional concept of almost squareness in order to provide a partial negative answer to the problem of existence of any dual almost square Banach space. We also…
Compact convex sets that admit a lower semicontinuous strictly convex function
L. García-Lirola, J. Orihuela, M. Raja
We study the class of compact convex subsets of a topological vector space which admits a strictly convex and lower semicontinuous function. We prove that such a compact set is emb…