| Title:
|
Multilinear operators on $C(K,X)$ spaces (English) |
| Author:
|
Villanueva, Ignacio |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
54 |
| Issue:
|
1 |
| Year:
|
2004 |
| Pages:
|
31-54 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Given Banach spaces~ $X$, $Y$ and a compact Hausdorff space~ $K$, we use polymeasures to give necessary conditions for a multilinear operator from $C(K,X)$ into~ $Y$ to be completely continuous (resp.~ unconditionally converging). We deduce necessary and sufficient conditions for~ $X$ to have the Schur property (resp.~ to contain no copy of~ $c_0$), and for~ $K$ to be scattered. This extends results concerning linear operators. (English) |
| Keyword:
|
completely continuous |
| Keyword:
|
unconditionally converging |
| Keyword:
|
multilinear operators |
| Keyword:
|
$C(K,X)$ spaces |
| MSC:
|
46B25 |
| MSC:
|
46G10 |
| MSC:
|
46G25 |
| MSC:
|
47B07 |
| MSC:
|
47H60 |
| idZBL:
|
Zbl 1050.46032 |
| idMR:
|
MR2040217 |
| . |
| Date available:
|
2009-09-24T11:09:23Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133372 |
| . |
| Reference:
|
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