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Extreme Cases of Limit Operator Theory on Metric Spaces

  • Jiawen Zhang
Open Access
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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 remaining extreme cases of \(p \in \{0,1,\infty \}\) (in the metric setting) to fill the gaps.

Keywords

Band-dominated operators Limit operators Property A 

Mathematics Subject Classification

47A53 30Lxx 46L85 47B36 

Notes

Acknowledgements

First, I would like to thank Kang Li for suggesting this topic and some early discussions. I am also grateful to Ján Špakula, Baojie Jiang and Benyin Fu for several illuminating discussions and comments after reading some early drafts of this paper. I would like to express my sincere gratitude to Graham Niblo and Nick Wright for continuous support. Finally, I would like to thank the anonymous referee for several helpful suggestions.

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Copyright information

© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.School of MathematicsUniversity of SouthamptonHighfieldUK

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