Some compact-like properties in non-archimedean functional analysis
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2022
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912211843153920 |
|---|---|
| author | Ishizuka, Kosuke |
| author_facet | Ishizuka, Kosuke |
| contents | First, we define some concepts similar to the local compactoidity or the c-compactness, and study relationships between these concepts and the original ones. As a result, we find a characterization of the local compactoidity when its coefficient field is spherically complete. Moreover, from the point of view of the minimum principle, we give a necessary and sufficient condition for the c-compactness under a suitable condition. Secondly, we try a new approach to a non-complete local compactoid, which gives us a different perspective than before. Thirdly, we study the non-archimedean Goldstine theorem and Eberlein-Smulian theorem. Consequently, if the coefficient field is spherically complete, we get results completely different from the classical ones. Finally, we give a new result about the closed range theorem by using epicompactness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_13476 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Some compact-like properties in non-archimedean functional analysis Ishizuka, Kosuke Functional Analysis 46S10, 12J25 First, we define some concepts similar to the local compactoidity or the c-compactness, and study relationships between these concepts and the original ones. As a result, we find a characterization of the local compactoidity when its coefficient field is spherically complete. Moreover, from the point of view of the minimum principle, we give a necessary and sufficient condition for the c-compactness under a suitable condition. Secondly, we try a new approach to a non-complete local compactoid, which gives us a different perspective than before. Thirdly, we study the non-archimedean Goldstine theorem and Eberlein-Smulian theorem. Consequently, if the coefficient field is spherically complete, we get results completely different from the classical ones. Finally, we give a new result about the closed range theorem by using epicompactness. |
| title | Some compact-like properties in non-archimedean functional analysis |
| topic | Functional Analysis 46S10, 12J25 |
| url | https://arxiv.org/abs/2207.13476 |