| Title:
|
Property $ \bf{(wL)}$ and the reciprocal Dunford-Pettis property in projective tensor products (English) |
| Author:
|
Ghenciu, Ioana |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
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0010-2628 (print) |
| ISSN:
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1213-7243 (online) |
| Volume:
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56 |
| Issue:
|
3 |
| Year:
|
2015 |
| Pages:
|
319-329 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A Banach space $X$ has the reciprocal Dunford-Pettis property ($RDPP$) if every completely continuous operator $T$ from $X$ to any Banach space $Y$ is weakly compact. A Banach space $X$ has the $RDPP$ (resp. property $(wL)$) if every $L$-subset of $X^*$ is relatively weakly compact (resp. weakly precompact). We prove that the projective tensor product $X \otimes{_\pi} Y$ has property $(wL)$ when $X$ has the $RDPP$, $Y$ has property $(wL)$, and $L(X,Y^*)=K(X,Y^*)$. (English) |
| Keyword:
|
the reciprocal Dunford-Pettis property |
| Keyword:
|
property $(wL)$ |
| Keyword:
|
spaces of compact operators |
| Keyword:
|
weakly precompact sets |
| MSC:
|
28B05 |
| MSC:
|
46B20 |
| MSC:
|
46B28 |
| idZBL:
|
Zbl 06486996 |
| idMR:
|
MR3390279 |
| DOI:
|
10.14712/1213-7243.2015.126 |
| . |
| Date available:
|
2015-07-09T20:47:20Z |
| Last updated:
|
2017-10-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144347 |
| . |
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