| Title:
|
A simple proof of the Borel extension theorem and weak compactness of operators (English) |
| Author:
|
Dobrakov, I. |
| Author:
|
Panchapagesan, T. V. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
52 |
| Issue:
|
4 |
| Year:
|
2002 |
| Pages:
|
691-703 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $T$ be a locally compact Hausdorff space and let $C_0(T)$ be the Banach space of all complex valued continuous functions vanishing at infinity in $T$, provided with the supremum norm. Let $X$ be a quasicomplete locally convex Hausdorff space. A simple proof of the theorem on regular Borel extension of $X$-valued $\sigma $-additive Baire measures on $T$ is given, which is more natural and direct than the existing ones. Using this result the integral representation and weak compactness of a continuous linear map $u\: C_0(T) \rightarrow X$ when $c_0 \lnot \subset X$ are obtained. The proof of the latter result is independent of the use of powerful results such as Theorem 6 of [6] or Theorem 3 (vii) of [13]. (English) |
| Keyword:
|
weakly compact operator on $C_0(T)$ |
| Keyword:
|
representing measure |
| Keyword:
|
lcHs-valued $\sigma $-additive Baire (or regular Borel |
| Keyword:
|
or regular $\sigma $-Borel) measures |
| MSC:
|
28B05 |
| MSC:
|
28C05 |
| MSC:
|
28C15 |
| MSC:
|
47B07 |
| idZBL:
|
Zbl 1023.28005 |
| idMR:
|
MR1940050 |
| . |
| Date available:
|
2009-09-24T10:55:35Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127755 |
| . |
| 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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| Reference:
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| Reference:
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