Guillaume Grelier

activity

20222024

collaborators

3 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

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.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…

Approximative compactness in Böchner spaces

Ergodicity and super weak compactness

Proximinality and uniformly approximable sets in Lp

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