| Title:
|
The positive cone of a Banach lattice. Coincidence of topologies and metrizability (English) |
| Author:
|
Lipecki, Zbigniew |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
64 |
| Issue:
|
4 |
| Year:
|
2023 |
| Pages:
|
475-483 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $X$ be a Banach lattice, and denote by $X_+$ its positive cone. The weak topology on $X_+$ is metrizable if and only if it coincides with the strong topology if and only if $X$ is Banach-lattice isomorphic to $l^1(\Gamma)$ for a set $\Gamma$. The weak$^*$ topology on $X_+^*$ is metrizable if and only if $X$ is Banach-lattice isomorphic to a $C(K)$-space, where $K$ is a metrizable compact space. (English) |
| Keyword:
|
normed lattice |
| Keyword:
|
Banach lattice |
| Keyword:
|
positive cone |
| Keyword:
|
AM-space |
| Keyword:
|
AL-space |
| Keyword:
|
Banach lattice $C(K)$ |
| Keyword:
|
Banach lattice $l^1(\Gamma)$ |
| Keyword:
|
strong topology |
| Keyword:
|
weak topology |
| Keyword:
|
weak$^*$ topology |
| Keyword:
|
coincidence of topologies |
| Keyword:
|
metrizability |
| Keyword:
|
nonatomic measure |
| MSC:
|
46B42 |
| MSC:
|
46E05 |
| MSC:
|
54E35 |
| idZBL:
|
Zbl 07953694 |
| idMR:
|
MR4813798 |
| DOI:
|
10.14712/1213-7243.2024.004 |
| . |
| Date available:
|
2024-11-05T11:50:31Z |
| Last updated:
|
2026-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/152626 |
| . |
| 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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| Reference:
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| Reference:
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| Reference:
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| . |
