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Quasinormability and property $(\Omega)$ for spaces of smooth and ultradifferentiable vectors associated to Lie group representations
We show that the spaces of smooth and ultradifferentiable vectors associated to a Lie group representation on a Fr\'echet space $E$ is quasinormable if $E$ is so. A similar result is shown for the linear topological invariant $(\Omega)$. In the ultradifferentiable case, our results particularly apply to spaces of Gevrey …