On asymptotics for $C_0$-semigroups

Abstract

We stretch the spectral bound equal growth bound condition along with a generalized Lyapunov stability theorem, known to hold for $C_0$-semigroups of normal operators on complex Hilbert spaces, to $C_0$-semigroups of scalar type spectral operators on complex Banach spaces. For such semigroups, we obtain exponential estimates with the best stability constants. We also extend to a Banach space setting a celebrated characterization of uniform exponential stability for $C_0$-semigroups on complex Hilbert spaces and thereby acquire a characterization of uniform exponential stability for scalar type spectral and eventually norm-continuous $C_0$-semigroups.

Various readability improvements. There is a text overlap with arXiv:2002.09087 in the Preliminaries section containing introductory information, definitions, and general remarks. arXiv admin note: substantial text overlap with arXiv:2002.09087

References in corpus (1)

• On the regularity of scalar type spectral $C_0$-semigroups