References & Citations
Mathematics > Functional Analysis
Title: Quasinormability and property $(Ω)$ for spaces of smooth and ultradifferentiable vectors associated to Lie group representations
(Submitted on 13 Mar 2024 (this version), latest version 27 Mar 2024 (v2))
Abstract: 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 vectors of order $\lambda >1$ of Beurling type. As an application, we study the quasinormability and the property $(\Omega)$ for a broad class of weighted spaces of smooth and ultradifferentiable functions on Lie groups.
Submission history
From: Andreas Debrouwere [view email][v1] Wed, 13 Mar 2024 07:07:22 GMT (34kb)
[v2] Wed, 27 Mar 2024 06:56:35 GMT (27kb)
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