Some translation-invariant Banach function spaces which contain $c_0$

TL;DR

This paper investigates specific translation-invariant Banach function spaces on compact abelian groups that include the space c_0, highlighting their structural properties and subspace relationships.

Contribution

It introduces new instances of Banach function spaces containing c_0, expanding understanding of their structure and subspace inclusions.

Findings

Identification of conditions under which these spaces contain c_0

Examples of classical Banach spaces with c_0 subspaces

Insights into the structure of translation-invariant Banach spaces

Abstract

We produce several situations where some natural subspaces of classical Banach spaces of functions over a compact abelian group contain the space $c_0$.