Marat V. Markin
Published 2021-07-06Version 1
We generalize to $C_0$-semigroups of scalar type spectral operators on complex Banach spaces 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. 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.
Comments: Written based on the part of arXiv:2002.09087v5 on asymptotics for semigroups, removed from arXiv:2002.09087, with new and modified statements. 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
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Interpolation and non-dilatable families of $C_{0}$-semigroups
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