# Limit operators techniques on general metric measure spaces of bounded geometry

## TL;DR

This paper develops a unified framework for limit operator techniques on metric measure spaces of bounded geometry, providing new insights and broadening applications in spectral analysis of band-dominated operators.

## Contribution

It introduces core assumptions for defining limit operators and characterizes compactness and Fredholmness in an abstract setting, unifying and extending classical results.

## Key findings

- Unified approach to limit operators on metric measure spaces
- Characterization of compactness and Fredholmness via limit operators
- Spectral consequences derived from the framework

## Abstract

We study band-dominated operators on (subspaces of) $L_p$-spaces over metric measure spaces of bounded geometry satisfying an additional property. We single out core assumptions to obtain, in an abstract setting, definitions of limit operators, characterizations of compactness and Fredholmness using limit operators; and thus also spectral consequences. In this way, we recover and unify the classical and recent results on limit operator techniques, but also gain new insights and are able to treat further applications.