arXiv subjects

Micheline Fakhoury

Publications and source records attributed to Micheline Fakhoury.

4 recordsLinked to original sources

arXiv2026

Isometric rigidity and Fraïssé properties of Orlicz sequence spaces

We provide an approximate version of a rigidity result by Randrianantoanina: for a large class of Orlicz sequence spaces, almost isometric embeddings almost preserve disjointness. In specific cases, we can even prove that such embeddings almost preserve basic vectors. As a consequence, we prove that some Orlicz sequences spaces are guarded Fraïssé but not $ω$-categorical; moreover, they do not contain copies of $\ell_2$ and their age is not closed. This answers a question of Cúth-de Rancourt-Doucha.

math.FA↗

arXiv2024

Tingley's problem for Schreier spaces and their $p$-convexifications

We describe the surjective isometries of the unit sphere of real Schreier spaces of all orders and their $p$-convexifications, for $1 < p < \infty$. This description allows us to provide for those spaces a positive answer to a special case of Tingley's problem, which asks whether every surjective isometry of the unit sphere of a real Banach space can be extended to a linear isometry of the entire space.

math.FA↗

arXiv2023

Isometries of $p$-convexified combinatorial Banach spaces

We show that if $1<p\neq 2<\infty$, then any isometry of the $p$-convexification of the combinatorial Banach space associated with a hereditary family of finite subsets of $\mathbb{N}$ containing the singletons is given by a signed permutation of the canonical basis. In the case of a generalized Schreier family, the result also holds for $p=2$, and every isometry is diagonal. These results are deduced from more general theorems concerning combinatorial-like Banach spaces.

math.FA↗

arXiv2022

Plasticity of the unit ball of some $C(K)$ spaces

We show that if $K$ is a compact metrizable space with finitely many accumulation points, then the closed unit ball of $C(K)$ is a plastic metric space, which means that any non-expansive bijection from $B_{C(K)}$ onto itself is in fact an isometry. We also show that if $K$ is a zero-dimensional compact Hausdorff space with a dense set of isolated points, then any non-expansive homeomorphism of $B_{C(K)}$ is an isometry.

math.FA↗