Tauberian Theorems and Stability of One-Parameter Semigroups

W. Arendt, C. J. K. Batty
1988 Transactions of the American Mathematical Society  
The main result is the following stability theorem: Let T = (T(f))(>0 be a bounded Co-semigroup on a reflexive space X. Denote by A the generator of T and by a(A) the spectrum of A. If c(A) n ¿R is countable and no eigenvalue of A lies on the imaginary axis, then limt^oo T(t)x = 0 for all x e X.
doi:10.2307/2000826 fatcat:dfiasjix6rbg7lgd7tarjwcoxm