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

TL;DR

This paper proves that the unit ball of the Banach space c is highly rigid under non-expansive bijections, which are necessarily isometries, and establishes similar results for c_0 with additional conditions.

Contribution

It establishes the plasticity of the unit ball of c and a related property for c_0, advancing understanding of geometric rigidity in Banach spaces.

Findings

Non-expansive bijections on the unit ball of c are isometries.

Non-expansive bijections with continuous inverse on the unit ball of c_0 are isometries.

The unit ball of c exhibits a strong form of geometric rigidity.

Abstract

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.