On a perturbation theorem of Kaiser and Weis (Q2571038)

The author answers a question of \textit{C.~Kaiser} and \textit{L.~Weis} [Semigroup Forum 67, No.~1, 63--75 (2003; Zbl 1046.47037)] concerning the strong continuity at \(t = 0\) of a semigroup generated by \(A+B\) on a Hilbert space \(X\), where \(A\) is the generator of a \(C_0\)-semigroup and \(B\) is some closed \(A\)-relatively bounded perturbation.