On the completeness of the space $\mathcal{O}_C$
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911345506516992 |
|---|---|
| author | Kunzinger, Michael Ortner, Norbert |
| author_facet | Kunzinger, Michael Ortner, Norbert |
| contents | We give a new proof of the completeness of the space $\mathcal{O}_C$ by applying a criterion of compact regularity for the isomorphic sequence space $\lim_{k\rightarrow} (s\hat \otimes (\ell^\infty)_{-k})$. Along the way we show that the strong dual of any quasinormable Fréchet space is a compactly regular $\mathcal{LB}$-space. Finally, we prove that $\lim_{k\rightarrow}(E_k\hat \otimes_ιF) = (\lim_{k\rightarrow} E_k) \hat \otimes_ιF$ if the inductive limit $\lim_{k \rightarrow}(E_k \hat \otimes_ιF)$ is compactly regular. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_11944 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the completeness of the space $\mathcal{O}_C$ Kunzinger, Michael Ortner, Norbert Functional Analysis 46A04, 46A08, 46A13, 46F05, 46F10 We give a new proof of the completeness of the space $\mathcal{O}_C$ by applying a criterion of compact regularity for the isomorphic sequence space $\lim_{k\rightarrow} (s\hat \otimes (\ell^\infty)_{-k})$. Along the way we show that the strong dual of any quasinormable Fréchet space is a compactly regular $\mathcal{LB}$-space. Finally, we prove that $\lim_{k\rightarrow}(E_k\hat \otimes_ιF) = (\lim_{k\rightarrow} E_k) \hat \otimes_ιF$ if the inductive limit $\lim_{k \rightarrow}(E_k \hat \otimes_ιF)$ is compactly regular. |
| title | On the completeness of the space $\mathcal{O}_C$ |
| topic | Functional Analysis 46A04, 46A08, 46A13, 46F05, 46F10 |
| url | https://arxiv.org/abs/2408.11944 |