Stability of uniformly eventually positive $C_0$-semigroups on $L_p$-spaces

Abstract

We give a short and elementary proof of the theorem of Lutz Weis 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 in corpus (3)

• Eventually Positive Semigroups of Linear Operators
• A criterion for the uniform eventual positivity of operator semigroups
• Sharp growth rates for semigroups using resolvent bounds

Cited by in corpus (2)

• Stability of (eventually) positive semigroups on spaces of continuous functions
• Criteria for eventual domination of operator semigroups and resolvents