| Title:
|
C*-algebras have a quantitative version of Pełczyński's property (V) (English) |
| Author:
|
Krulišová, Hana |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
67 |
| Issue:
|
4 |
| Year:
|
2017 |
| Pages:
|
937-951 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A Banach space $X$ has Pełczyński's property (V) if for every Banach space $Y$ every unconditionally converging operator $T\colon X\to Y$ is weakly compact. H. Pfitzner proved that $C^*$-algebras have Pełczyński's property (V). In the preprint (Krulišová, (2015)) the author explores possible quantifications of the property (V) and shows that $C(K)$ spaces for a compact Hausdorff space $K$ enjoy a quantitative version of the property (V). In this paper we generalize this result by quantifying Pfitzner's theorem. Moreover, we prove that in dual Banach spaces a quantitative version of the property (V) implies a quantitative version of the Grothendieck property. (English) |
| Keyword:
|
Pełczyński's property (V) |
| Keyword:
|
$C^*$-algebra |
| Keyword:
|
Grothendieck property |
| MSC:
|
46B04 |
| MSC:
|
46L05 |
| MSC:
|
47B10 |
| idZBL:
|
Zbl 06819564 |
| idMR:
|
MR3736010 |
| DOI:
|
10.21136/CMJ.2017.0242-16 |
| . |
| Date available:
|
2017-11-20T14:53:02Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146958 |
| . |
| 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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| . |
