## Krein–Rutman type property and exponential separation of a noncompact operator

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- by Lirui Feng and Jianhong Wu
- Proc. Amer. Math. Soc.
**147**(2019), 4771-4780 - 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.## References

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## Bibliographic 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
- 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
- © Copyright 2019 American Mathematical Society
- 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
- MathSciNet review: 4011511