Nontrivial twisted sums of $c_0$ and $C(K)$

TL;DR

This paper introduces a new class of compact Hausdorff spaces where the Banach space $c_0$ can be nontrivially twisted with the space of continuous functions $C(K)$, expanding understanding of their structural relationships.

Contribution

It identifies a novel class of spaces $K$ for which $c_0$ admits nontrivial twisted sums with $C(K)$, advancing the theory of Banach space extensions.

Findings

Established existence of nontrivial twisted sums for new class of $K$

Extended the class of spaces where $c_0$ and $C(K)$ are nontrivially related

Provided new examples of twisted sums in Banach space theory

Abstract

We obtain a new class of compact Hausdorff spaces $K$ for which $c_0$ can be nontrivially twisted with $C(K)$.