On the plasticity of the unit spheres of $\ell_1$, $\ell_{\infty}$, $c$, and Hilbert spaces

TL;DR

This paper investigates the geometric property of plasticity of unit spheres in various classical Banach spaces, showing expand-contract plasticity in some and strong plasticity in Hilbert spaces.

Contribution

It establishes the expand-contract plasticity for unit spheres of $\, ext{l}_1$, $ ext{l}_ ext{infinity}$, and $c$, and proves strong plasticity for Hilbert space unit spheres.

Findings

Unit spheres of $ ext{l}_1$, $ ext{l}_ ext{infinity}$, and $c$ are expand-contract plastic.

Unit spheres of Hilbert spaces are strongly plastic.

These results deepen understanding of geometric properties of classical Banach spaces.

Abstract

This paper demonstrates the expand-contract plasticity of the unit spheres of $\ell_1$, $\ell_{\infty}$, and $c$. Furthermore, it establishes the strong plasticity of the unit spheres of Hilbert spaces.