Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.17385 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913951665618944 |
|---|---|
| author | Ishizuka, Kosuke |
| author_facet | Ishizuka, Kosuke |
| contents | In this paper, we will establish a general method of studying finite-dimensional normed spaces, and apply this method to classifying $3$-dimensional and $4$-dimensional normed spaces over a non-spherically complete field. For this purpose, we will use the spherical completion. From the perspective of the spherical completion, each finite-dimensional normed space can be embedded into a simple space. In order to study simple spaces, the orthogonality is important. The orthogonality allows us to find a classification of finite-dimensional normed spaces. As an application of our study, we can get a characterization of strictly epicompact sets, which is an open problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_17385 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An application of the spherical completion to finite-dimensional normed spaces Ishizuka, Kosuke Functional Analysis 46S10 (Primary), 12J25 (Secondary) In this paper, we will establish a general method of studying finite-dimensional normed spaces, and apply this method to classifying $3$-dimensional and $4$-dimensional normed spaces over a non-spherically complete field. For this purpose, we will use the spherical completion. From the perspective of the spherical completion, each finite-dimensional normed space can be embedded into a simple space. In order to study simple spaces, the orthogonality is important. The orthogonality allows us to find a classification of finite-dimensional normed spaces. As an application of our study, we can get a characterization of strictly epicompact sets, which is an open problem. |
| title | An application of the spherical completion to finite-dimensional normed spaces |
| topic | Functional Analysis 46S10 (Primary), 12J25 (Secondary) |
| url | https://arxiv.org/abs/2412.17385 |