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It is shown that, if all weak solutions of the evolution equation\begin{equation*} y'(t)=Ay(t),\ t\ge0, \end{equation*} with a scalar typespectral operator $A$ in a complex Banach space are Gevrey ultradifferentiableof orders less than one, then the operator $A$ is necessarily bounded.

On the Gevrey ultradifferentiability of weak solutions of an abstract  evolution equation with a scalar type spectral operator of orders less than  one