| Title:
|
Banach spaces of homogeneous polynomials without the approximation property (English) |
| Author:
|
Dineen, Seán |
| Author:
|
Mujica, Jorge |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
65 |
| Issue:
|
2 |
| Year:
|
2015 |
| Pages:
|
367-374 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We present simple proofs that spaces of homogeneous polynomials on $L_{p}[0,1]$ and $\ell _{p}$ provide plenty of natural examples of Banach spaces without the approximation property. By giving necessary and sufficient conditions, our results bring to completion, at least for an important collection of Banach spaces, a circle of results begun in 1976 by R. Aron and M. Schottenloher (1976). (English) |
| Keyword:
|
Banach space |
| Keyword:
|
approximation property |
| Keyword:
|
linear operator |
| Keyword:
|
homogeneous polynomial |
| Keyword:
|
holomorphic function |
| MSC:
|
46B28 |
| MSC:
|
46G20 |
| MSC:
|
46G25 |
| idZBL:
|
Zbl 06486952 |
| idMR:
|
MR3360432 |
| DOI:
|
10.1007/s10587-015-0181-6 |
| . |
| Date available:
|
2015-06-16T17:44:06Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144275 |
| . |
| Reference:
|
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