Limit operators techniques on general metric measure spaces of bounded geometry

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:489

Article

Hagger, Raffael^1,2  Seifert, Christian^3,4 

[1] Leibniz Univ Hannover, Fak Math & Phys, Fachgebiet Math, Welfengarten 1, D-30167 Hannover, Germany

[2] Univ Reading, Dept Math & Stat, POB 220, Reading RG6 6AX, Berks, England

[3] Tech Univ Hamburg, Inst Math, Schwarzenberg Campus 3, D-21073 Hamburg, Germany

[4] Tech Univ Clausthal, Inst Math, Erzstr 1, D-38678 Clausthal Zellerfeld, Germany

关键词: Metric measure spaces;    Bounded geometry;    Limit operators;    Fredholm;    Essential spectrum;   

DOI  :  10.1016/j.jmaa.2020.124180

来源: Elsevier

【 摘 要 】

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. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free