Year: 1988
Type: article
Abstract: The main result is the following stability theorem: Let $\mathcal {T} = {(T(t))_{t \geqslant 0}}$ be a bounded ${C_0}$-semigroup on a reflexive space $X$. Denote by $A$ the generator of $\mathcal {T}$ and by $\sigma (A)$ the spectrum of $A$. If $\sigma (A) \cap i{\mathbf {R}}$ is countable and no eigenvalue of $A$ lies on the imaginary axis, then ${\lim _{t \to \infty }}T(t)x = 0$ for all $x \in X$.
Authors: W. Arendt, C. J. K. Batty
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2034128352