On the properties of quasi-Banach function spaces
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2020
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866917854727634944 |
|---|---|
| author | Nekvinda, Aleš Peša, Dalimil |
| author_facet | Nekvinda, Aleš Peša, Dalimil |
| contents | In this paper we explore some basic properties of quasi-Banach function spaces which are important in applications. Namely, we show that they posses a generalised version of Riesz--Fischer property, that embeddings between them are always continuous and that the dilation operator is bounded on them. We also provide a characterisation of separability for quasi-Banach function spaces over the Euclidean space. Furthermore, we extend the classical Riesz--Fischer theorem to the context of quasinormed spaces and, as a consequence, obtain an alternative proof of completeness of quasi-Banach function spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2004_09435 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On the properties of quasi-Banach function spaces Nekvinda, Aleš Peša, Dalimil Functional Analysis 46A16, 46E30 In this paper we explore some basic properties of quasi-Banach function spaces which are important in applications. Namely, we show that they posses a generalised version of Riesz--Fischer property, that embeddings between them are always continuous and that the dilation operator is bounded on them. We also provide a characterisation of separability for quasi-Banach function spaces over the Euclidean space. Furthermore, we extend the classical Riesz--Fischer theorem to the context of quasinormed spaces and, as a consequence, obtain an alternative proof of completeness of quasi-Banach function spaces. |
| title | On the properties of quasi-Banach function spaces |
| topic | Functional Analysis 46A16, 46E30 |
| url | https://arxiv.org/abs/2004.09435 |