Extreme contractions on finite-dimensional Banach spaces
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909285869420544 |
|---|---|
| author | Sain, Debmalya Sohel, Shamim Paul, Kallol |
| author_facet | Sain, Debmalya Sohel, Shamim Paul, Kallol |
| contents | We study extreme contractions in the setting of finite-dimensional polyhedral Banach spaces. Motivated by the famous Krein-Milman Theorem, we prove that a \emph{rank one} norm one linear operator between such spaces can be expressed as a convex combination of \emph{rank one} extreme contractions, whenever the domain is two-dimensional. We establish that the same result holds true in the space of all linear operators from $\ell_{\infty}^n(\mathbb{C}) $ to $ \ell_1^n (\mathbb{C}). $ Furthermore, we present a geometric characterization of extreme contractions between finite-dimensional polyhedral Banach spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_05545 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Extreme contractions on finite-dimensional Banach spaces Sain, Debmalya Sohel, Shamim Paul, Kallol Functional Analysis 46B20, 47L05 We study extreme contractions in the setting of finite-dimensional polyhedral Banach spaces. Motivated by the famous Krein-Milman Theorem, we prove that a \emph{rank one} norm one linear operator between such spaces can be expressed as a convex combination of \emph{rank one} extreme contractions, whenever the domain is two-dimensional. We establish that the same result holds true in the space of all linear operators from $\ell_{\infty}^n(\mathbb{C}) $ to $ \ell_1^n (\mathbb{C}). $ Furthermore, we present a geometric characterization of extreme contractions between finite-dimensional polyhedral Banach spaces. |
| title | Extreme contractions on finite-dimensional Banach spaces |
| topic | Functional Analysis 46B20, 47L05 |
| url | https://arxiv.org/abs/2407.05545 |