Quasinormability and property $(Ω)$ for spaces of smooth and ultradifferentiable vectors associated with Lie group representations
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911815602012160 |
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| author | Debrouwere, Andreas Huttener, Michiel Vindas, Jasson |
| author_facet | Debrouwere, Andreas Huttener, Michiel Vindas, Jasson |
| contents | We prove that the spaces of smooth and ultradifferentiable vectors associated with a representation of a real Lie group on a Fréchet space $E$ are quasinormable if $E$ is so. A similar result is shown to hold for the linear topological invariant $(Ω)$. 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 $(Ω)$ for a broad class of Fréchet spaces of smooth and ultradifferentiable functions on Lie groups globally defined via families of weight functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_08296 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quasinormability and property $(Ω)$ for spaces of smooth and ultradifferentiable vectors associated with Lie group representations Debrouwere, Andreas Huttener, Michiel Vindas, Jasson Functional Analysis 46E10, 46A63, 22E30 (Primary) 43A15, 46E40 (Secondary) We prove that the spaces of smooth and ultradifferentiable vectors associated with a representation of a real Lie group on a Fréchet space $E$ are quasinormable if $E$ is so. A similar result is shown to hold for the linear topological invariant $(Ω)$. 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 $(Ω)$ for a broad class of Fréchet spaces of smooth and ultradifferentiable functions on Lie groups globally defined via families of weight functions. |
| title | Quasinormability and property $(Ω)$ for spaces of smooth and ultradifferentiable vectors associated with Lie group representations |
| topic | Functional Analysis 46E10, 46A63, 22E30 (Primary) 43A15, 46E40 (Secondary) |
| url | https://arxiv.org/abs/2403.08296 |