Separably injective $C_\sigma$-spaces

TL;DR

This paper characterizes when complex $C_\sigma$-spaces are separably injective, showing they are exactly those isometric to $C_0(\Omega)$ on substonean spaces, linking geometric and topological properties.

Contribution

It provides a complete characterization of separably injective complex $C_\sigma$-spaces in terms of their isometric relation to $C_0(\Omega)$ spaces on substonean spaces.

Findings

Separable injectivity is equivalent to being isometric to $C_0(\Omega)$ on substonean spaces.

Provides a topological characterization of complex $C_\sigma$-spaces with this property.

Links geometric Banach space properties with topological space classifications.

Abstract

We show that a (complex) $C_\sigma$-space is separably injective if and only if it is linearly isometric to the Banach space $C_0(\Omega)$ of complex continuous functions vanishing at infinity on a substonean locally compact Hausdorff space $\Omega$.