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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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A metric approach to limit operators
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by Ján Špakula and Rufus Willett PDF
Trans. Amer. Math. Soc. 369 (2017), 263-308 Request permission

Abstract:

We extend the limit operator machinery of Rabinovich, Roch, and Silbermann from $\mathbb {Z}^N$ to (bounded geometry, strongly) discrete metric spaces. We do not assume the presence of any group structure or action on our metric spaces. Using this machinery and recent ideas of Lindner and Seidel, we show that if a metric space $X$ has Yu’s property A, then a band-dominated operator on $X$ is Fredholm if and only if all of its limit operators are invertible. We also show that this always fails for metric spaces without property A.
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Additional Information
  • Ján Špakula
  • Affiliation: Mathematical Sciences, University of Southampton, SO17 1BJ, United Kingdom
  • MR Author ID: 751861
  • Email: jan.spakula@soton.ac.uk
  • Rufus Willett
  • Affiliation: Department of Mathematics, 2565 McCarthy Mall, University of Hawai\kern.05em’\kern.05emi at Mānoa, Honolulu, Hawaii 96822
  • MR Author ID: 882807
  • Email: rufus.willett@hawaii.edu
  • Received by editor(s): September 11, 2014
  • Received by editor(s) in revised form: December 18, 2014
  • Published electronically: March 2, 2016
  • Additional Notes: The second author was partially supported by the US NSF
  • © Copyright 2016 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 369 (2017), 263-308
  • MSC (2010): Primary 47A53; Secondary 30Lxx, 46L85, 47B36
  • DOI: https://doi.org/10.1090/tran/6660
  • MathSciNet review: 3557774