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Krein-Rutman type property and exponential separation of a noncompact operator


Authors: Lirui Feng and Jianhong Wu
Journal: Proc. Amer. Math. Soc. 147 (2019), 4771-4780
MSC (2000): Primary 37C35, 37C65, 37D30; Secondary 35K57, 35K65
DOI: https://doi.org/10.1090/proc/14556
Published electronically: July 30, 2019
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Abstract: We investigate exponentially separated property for a noncompact linear operator $ T$ on a Banach space. We obtain the relationship between exponentially separated property and the well-known Krein-Rutman type property for a noncompact operator. Under the assumption of an essential spectral gap, we prove that any $ u$-bounded operator $ T$ with a reproducing cone admits the exponentially separated property and, hence, is of Krein-Rutman type automatically. We also establish an amenable sufficient condition for the exponentially separated property of some degenerate linear parabolic systems.


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Additional Information

Lirui Feng
Affiliation: Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada M3J1P3
Email: flrui18@yorku.ca

Jianhong Wu
Affiliation: Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada M3J1P3
Email: wujh@mathstat.yorku.ca

DOI: https://doi.org/10.1090/proc/14556
Keywords: Exponential separation, noncompact operators, Krein--Rutman type property
Received by editor(s): December 6, 2018
Received by editor(s) in revised form: December 6, 2018, and January 8, 2019
Published electronically: July 30, 2019
Additional Notes: Both authors were supported by the NSERC and the NSERC-IRC Program
The second author was supported by NSERC 105588-2011
Communicated by: Wenxian Shen
Article copyright: © Copyright 2019 American Mathematical Society