A metric approach to limit operators
A metric approach to limit operators
We extend the limit operator machinery of Rabinovich, Roch, and Silbermann from 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
263-308
Spakula, Jan
c43164e4-36a7-4372-9ce2-9bfbba775d77
Willett, Rufus
9f00bf4a-53ab-47b5-9f59-d12174765907
January 2017
Spakula, Jan
c43164e4-36a7-4372-9ce2-9bfbba775d77
Willett, Rufus
9f00bf4a-53ab-47b5-9f59-d12174765907
Spakula, Jan and Willett, Rufus
(2017)
A metric approach to limit operators.
Transactions of the American Mathematical Society, 369, .
(doi:10.1090/tran/6660).
Abstract
We extend the limit operator machinery of Rabinovich, Roch, and Silbermann from 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
Text
metriclimops2.pdf
- Accepted Manuscript
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e-pub ahead of print date: 2 March 2016
Published date: January 2017
Organisations:
Pure Mathematics
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Local EPrints ID: 373544
URI: http://eprints.soton.ac.uk/id/eprint/373544
ISSN: 0002-9947
PURE UUID: 3cfac1b3-77fc-4fd4-af16-60a15aaa4347
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Date deposited: 22 Jan 2015 11:28
Last modified: 15 Mar 2024 03:48
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Author:
Rufus Willett
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