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Shnol's theorem and the spectrum of long range operators


Author: Rui Han
Journal: Proc. Amer. Math. Soc. 147 (2019), 2887-2897
MSC (2010): Primary 47B36; Secondary 81Q10
DOI: https://doi.org/10.1090/proc/14388
Published electronically: April 3, 2019
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Abstract: We extend some basic results known for finite range operators to long range operators with off-diagonal decay. Namely, we prove an analogue of Shnol's theorem. We also establish the connection between the almost sure spectrum of long range random operators and the spectra of deterministic periodic operators.


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Additional Information

Rui Han
Affiliation: Department of Mathematics, University of California, Irvine, Irvine, California 92697
Address at time of publication: School of Math, Georgia Institute of Technology, Atlanta, GA 30332
Email: rui.han2@math.gatech.edu

DOI: https://doi.org/10.1090/proc/14388
Received by editor(s): January 11, 2017
Received by editor(s) in revised form: July 28, 2018, and August 11, 2018
Published electronically: April 3, 2019
Additional Notes: This research was partially supported by the NSF DMS-1401204.
Communicated by: Michael Hitrik
Article copyright: © Copyright 2019 American Mathematical Society