| Title:
|
Unconditional ideals of finite rank operators (English) |
| Author:
|
Abrahamsen, Trond A. |
| Author:
|
Lima, Asvald |
| Author:
|
Lima, Vegard |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
58 |
| Issue:
|
4 |
| Year:
|
2008 |
| Pages:
|
1257-1278 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $X$ be a Banach space. We give characterizations of when ${\cal F}(Y,X)$ is a $u$-ideal in ${\cal W}(Y,X)$ for every Banach space $Y$ in terms of nets of finite rank operators approximating weakly compact operators. Similar characterizations are given for the cases when ${\cal F}(X,Y)$ is a $u$-ideal in ${\cal W}(X,Y)$ for every Banach space $Y$, when ${\cal F}(Y,X)$ is a $u$-ideal in ${\cal W}(Y,X^{**})$ for every Banach space $Y$, and when ${\cal F}(Y,X)$ is a $u$-ideal in ${\cal K}(Y,X^{**})$ for every Banach space $Y$. (English) |
| Keyword:
|
$u$-ideals |
| Keyword:
|
finite rank |
| Keyword:
|
compact |
| Keyword:
|
and weakly compact operators |
| Keyword:
|
Hahn-Banach extension operators |
| MSC:
|
46B04 |
| MSC:
|
46B20 |
| MSC:
|
46B28 |
| MSC:
|
47L20 |
| idZBL:
|
Zbl 1174.46003 |
| idMR:
|
MR2471182 |
| . |
| Date available:
|
2010-07-21T08:18:50Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140456 |
| . |
| Reference:
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