G. Grelier

activity

20212024

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Showing 2022Show all

4 papers · 1 filter

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…

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

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