Stability of uniformly eventually positive 𝐶₀-semigroups on 𝐿_{𝑝}-spaces

Vogt, Hendrik

doi:10.1090/proc/15926

Stability of uniformly eventually positive $C_0$-semigroups on $L_p$-spaces
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Proc. Amer. Math. Soc. 150 (2022), 3513-3515 Request permission

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.

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