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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
MathSciNet review: 4011511
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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
MR Author ID: 1193629
Email: flrui18@yorku.ca

Jianhong Wu
Affiliation: Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada M3J1P3
MR Author ID: 226643
Email: wujh@mathstat.yorku.ca

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