G. Grelier

activity

20212024

collaborators

10 papers

math.FA2024

Approximative compactness in Böchner spaces

Guillaume Grelier, Jaime San Martín

For any $p \in [1, \infty)$ , we prove that the set of simple functions taking at most $k$ different values is proximinal in Böchner spaces $L^{p} (X)$ whenever $X$ is a dual Banach space…

math.FA2023

A note on nonseparable Lipschitz-free spaces

Ramón J. Aliaga, Guillaume Grelier, Antonín Procházka

We prove that several classical Banach space properties are equivalent to separability for the class of Lipschitz-free spaces, including Corson's property ( $C$ ), Talponen…

math.FA2023

Ergodicity and super weak compactness

Guillaume Grelier, Matías Raja

We prove that a closed convex subset of a Banach space is (super-)weakly compact if and only if it is (super)-ergodic. As a consequence we deduce that super weakly compact sets are…

math.FA2023

Uniform Banach-Saks properties

G. Grelier

The principal aim of this paper is to study the Banach-Saks property when the speed of convergence of a Cesaro mean sequence can be chosen independtly from the choice of the initia…

math.FA2022

Extremal structure of projective tensor products

Luis C. García-Lirola, Guillaume Grelier, Gonzalo Martínez-Cervantes +1

We prove that, given two Banach spaces $X$ and $Y$ and bounded, closed convex sets $C \subseteq X$ and $D \subseteq Y$ , if a nonzero element $z\in \overline{\mathrm{co}}(C\otimes D)\…

math.CA2022

Proximinality and uniformly approximable sets in $L^{p}$

Guillaume Grelier, Jaime San Martín

For any $p \in [1, \infty]$ , we prove that the set of simple functions taking at most $k$ different values is proximinal in $L^{p}$ for all $k \geq 1$ . We introduce the class of uniforml…

math.FA2022

Lipschitz-free spaces, ultraproducts, and finite representability of metric spaces

Luis C. García-Lirola, G. Grelier

We study several properties and applications of the ultrapower $M_{U}$ of a metric space $M$ . We prove that the Lipschitz-free space $F (M_{U})$ is finite…

math.FA2022

Applications of the quantification of super weak compactness

Guillaume Grelier, Matías Raja

We introduce a measure of super weak noncompactness $Γ$ defined for bounded linear operators and subsets in Banach spaces that allows to state and prove a characterization of the B…

math.FA2021

Extremal structure in ultrapowers of Banach spaces

Luis C. García-Lirola, Guillaume Grelier, Abraham Rueda Zoca

Given a bounded convex subset $C$ of a Banach space $X$ and a free ultrafilter $U$ , we study which points $(x_{i})_{U}$ are extreme points of the ultrapower $C_\mathc…

math.FA2021

On uniformly convex functions

Guillaume Grelier, Matías Raja

Non-convex functions that yet satisfy a condition of uniform convexity for non-close points can arise in discrete constructions. We prove that this sort of discrete uniform convexi…

Approximative compactness in Böchner spaces

A note on nonseparable Lipschitz-free spaces

Ergodicity and super weak compactness

Uniform Banach-Saks properties

Extremal structure of projective tensor products

Proximinality and uniformly approximable sets in Lp

Lipschitz-free spaces, ultraproducts, and finite representability of metric spaces

Applications of the quantification of super weak compactness

Extremal structure in ultrapowers of Banach spaces

On uniformly convex functions

Proximinality and uniformly approximable sets in $L^{p}$