| Title:
|
The lattice copies of $\ell_1$ in Banach lattices (English) |
| Author:
|
Wójtowicz, Marek |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
42 |
| Issue:
|
4 |
| Year:
|
2001 |
| Pages:
|
649-653 |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is known that a Banach lattice with order continuous norm contains a copy of $\ell_1$ if and only if it contains a lattice copy of $\ell_1$. The purpose of this note is to present a more direct proof of this useful fact, which extends a similar theorem due to R.C. James for Banach spaces with unconditional bases, and complements the $c_0$- and $\ell_{\infty}$-cases considered by Lozanovskii, Mekler and Meyer-Nieberg. (English) |
| Keyword:
|
Banach lattice |
| Keyword:
|
order continuous norm |
| Keyword:
|
embedding of $\ell_1$ |
| MSC:
|
46B42 |
| MSC:
|
46B45 |
| idZBL:
|
Zbl 1090.46503 |
| idMR:
|
MR1883374 |
| . |
| Date available:
|
2009-01-08T19:17:21Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119281 |
| . |
| 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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| . |
