  Given the abstract evolution equation \[ y'(t)=Ay(t),\ t\in \mathbb{R}, \]
with a scalar type spectral operator $A$ in a complex Banach space, we find
conditions on $A$, formulated exclusively in terms of the location of its
spectrum in the complex plane, necessary and sufficient for all weak solutions
of the equation, which a priori need not be strongly differentiable, to be
strongly Gevrey ultradifferentiable of order $\beta\ge 1$, in particular
analytic or entire, on $\mathbb{R}$. We also reveal certain inherent smoothness
improvement effects and show that, if all weak solutions of the equation are
Gevrey ultradifferentiable of orders less than one, then the operator $A$ is
necessarily bounded. The important particular case of the equation with a
normal operator $A$ in a complex Hilbert space follows immediately.
