Extreme cases of limit operator theory on metric spaces

Abstract

The theory of limit operators was developed by Rabinovich, Roch and Silbermann to study the Fredholmness of band-dominated operators on ${\ell }^p({\mathbb{Z}}^N)$ for $p\in \{0\}\cup [1,\infty ]$, and recently generalised to discrete metric spaces with property A by Špakula and Willett for $p\in (1,\infty )$. In this paper, we study the remained extreme cases of $p\in \{0,1,\infty \}$ (in the metric setting) to fill the gaps.

26 pages