  Found are conditions on a scalar type spectral operator $A$ in a complex
Banach space necessary and sufficient for all weak solutions of the evolution
equation \begin{equation*} y'(t)=Ay(t),\ t\ge 0, \end{equation*} to be strongly
Gevrey ultradifferentiable of order $\beta\ge 1$, in particular analytic or
entire, on $[0,\infty)$. Certain inherent smoothness improvement effects are
analyzed.
