Article
| Title: | On the Banach-Mazur distance between continuous function spaces with scattered boundaries (English) |
| Author: | Rondoš, Jakub |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 73 |
| Issue: | 2 |
| Year: | 2023 |
| Pages: | 367-393 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We study the dependence of the Banach-Mazur distance between two subspaces of vector-valued continuous functions on the scattered structure of their boundaries. In the spirit of a result of Y. Gordon (1970), we show that the constant $2$ appearing in the Amir-Cambern theorem may be replaced by $3$ for some class of subspaces. We achieve this by showing that the Banach-Mazur distance of two function spaces is at least 3, if the height of the set of weak peak points of one of the spaces differs from the height of a closed boundary of the second space. Next we show that this estimate can be improved if the considered heights are finite and significantly different. As a corollary, we obtain new results even for the case of $\mathcal C(K, E)$ spaces. (English) |
| Keyword: | function space |
| Keyword: | vector-valued Amir-Cambern theorem |
| Keyword: | scattered space |
| Keyword: | Banach-Mazur distance |
| Keyword: | closed boundary |
| MSC: | 46A55 |
| MSC: | 46B03 |
| MSC: | 46E40 |
| idZBL: | Zbl 07729513 |
| idMR: | MR4586900 |
| DOI: | 10.21136/CMJ.2023.0220-21 |
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| Date available: | 2023-05-04T17:43:13Z |
| Last updated: | 2023-09-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151663 |
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