arXiv subjects

Nikita Leo

Publications and source records attributed to Nikita Leo.

3 recordsLinked to original sources

arXiv2026

Plasticity of the unit ball of the real Banach space $\ell_\infty$

We prove that the closed unit ball of the real Banach space $\ell_\infty$ is plastic, that is, every non-expansive bijection from the unit ball onto itself is an isometry. The main step is to show that every non-expansive bijection of this ball maps extreme points to extreme points. This is done by using elementary coverings of the unit ball by balls of radius one. The conclusion then follows from a theorem by Fakhoury. The same argument also shows that, for arbitrary $Γ$, every non-expansive bijection of $B_{\ell_\infty(Γ)}$ preserves extreme points.

math.FA↗

arXiv2021

Two new examples of Banach spaces with a plastic unit ball

We prove that Banach spaces $\ell_1\oplus_2\mathbb{R}$ and $X\oplus_\infty Y$, with strictly convex $X$ and $Y$, have plastic unit balls (we call a metric space plastic if every non-expansive bijection from this space onto itself is an isometry).

math.FA↗

arXiv2021

Plasticity of the unit ball of $c$ and $c_0$

We prove the plasticity of the unit ball of $c$. That is, we show that every non-expansive bijection from the unit ball of $c$ onto itself is an isometry. We also demonstrate a slightly weaker property for the unit ball of $c_0$ -- we prove that a non-expansive bijection is an isometry, provided that it has a continuous inverse.

math.FA↗