| Title:
|
On the diameter of the Banach-Mazur set (English) |
| Author:
|
Godefroy, Gilles |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
60 |
| Issue:
|
1 |
| Year:
|
2010 |
| Pages:
|
95-100 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
On every subspace of $l_{\infty }(\mathbb N)$ which contains an uncountable $\omega $-independent set, we construct equivalent norms whose Banach-Mazur distance is as large as required. Under Martin's Maximum Axiom (MM), it follows that the Banach-Mazur diameter of the set of equivalent norms on every infinite-dimensional subspace of $l_{\infty }(\mathbb N)$ is infinite. This provides a partial answer to a question asked by Johnson and Odell. (English) |
| Keyword:
|
Banach-Mazur diameter |
| Keyword:
|
elastic Banach spaces |
| Keyword:
|
Martin's Maximum axiom |
| MSC:
|
03E50 |
| MSC:
|
46B03 |
| MSC:
|
46B20 |
| MSC:
|
46B26 |
| idZBL:
|
Zbl 1224.46012 |
| idMR:
|
MR2595073 |
| . |
| Date available:
|
2010-07-20T16:17:23Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140552 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
