Extreme Cases of Limit Operator Theory on Metric Spaces

  • Jiawen ZhangEmail author
Open Access


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.


Band-dominated operators Limit operators Property A 

Mathematics Subject Classification

47A53 30Lxx 46L85 47B36 



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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© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, 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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