Separably injective C*-algebras

TL;DR

This paper characterizes separably injective C*-algebras as those linearly isometric to certain function spaces on substonean locally compact Hausdorff spaces, providing a precise structural description.

Contribution

It establishes a complete characterization of 1-separably injective C*-algebras in terms of isometric isomorphisms to specific function spaces.

Findings

A C*-algebra is 1-separably injective if and only if it is isometric to C_0(Ω) for a substonean space Ω.

Provides a structural classification linking injectivity to topological properties of the underlying space.

Clarifies the relationship between injectivity properties and the geometry of C*-algebras.

Abstract

We show that a C*-algebra is a $1$-separably injective Banach space 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 $\Omega$.