References & Citations
Mathematics > Functional Analysis
Title: Quasinormability and property $(Ω)$ for spaces of smooth and ultradifferentiable vectors associated with Lie group representations
(Submitted on 13 Mar 2024 (v1), last revised 27 Mar 2024 (this version, v2))
Abstract: We prove that the spaces of smooth and ultradifferentiable vectors associated with a representation of a real Lie group on a Fr\'{e}chet space $E$ are quasinormable if $E$ is so. A similar result is shown to hold for the linear topological invariant $(\Omega)$. In the ultradifferentiable case, our results particularly apply to spaces of Gevrey vectors of Beurling type. As an application, we study the quasinormability and the property $(\Omega)$ for a broad class of Fr\'{e}chet spaces of smooth and ultradifferentiable functions on Lie groups globally defined via families of weight functions.
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)
Link back to: arXiv, form interface, contact.