Stability of uniformly eventually positive $C_0$-semigroups on $L_p$-spaces
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Abstract:
We give a short and elementary proof of the theorem of Lutz Weis [Proc. Amer. Math. Soc. 123 (1995), pp. 3089–3094] that the growth bound of a positive $C_0$-semigroup on $L_p(\mu )$ equals the spectral bound of its generator. In addition, we generalise the result to the case of uniformly eventually positive semigroups.References
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Additional Information
- Hendrik Vogt
- Affiliation: Fachbereich 3 – Mathematik, Universität Bremen, 28359 Bremen, Germany
- MR Author ID: 636034
- Email: hendrik.vogt@uni-bremen.de
- Received by editor(s): October 5, 2021
- Received by editor(s) in revised form: November 9, 2021
- Published electronically: April 1, 2022
- Communicated by: Ariel Barton
- © Copyright 2022 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 150 (2022), 3513-3515
- MSC (2020): Primary 47D06, 47B65, 46G10
- DOI: https://doi.org/10.1090/proc/15926
- MathSciNet review: 4439472