| Title:
|
The continuity of superposition operators on some sequence spaces defined by moduli (English) |
| Author:
|
Kolk, Enno |
| Author:
|
Raidjõe, Annemai |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
57 |
| Issue:
|
3 |
| Year:
|
2007 |
| Pages:
|
777-792 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $\lambda $ and $\mu $ be solid sequence spaces. For a sequence of modulus functions $\Phi =(\varphi _{k})$ let $ \lambda (\Phi )= \lbrace x=(x_{k}) \: (\varphi _{k}(|x_{k}|))\in \lambda \rbrace $. Given another sequence of modulus functions $\Psi =(\psi _{k})$, we characterize the continuity of the superposition operators ${P_{f}}$ from $\lambda (\Phi )$ into $\mu (\Psi )$ for some Banach sequence spaces $\lambda $ and $\mu $ under the assumptions that the moduli $\varphi _{k}$ $(k \in \mathbb{N})$ are unbounded and the topologies on the sequence spaces $\lambda (\Phi )$ and $\mu (\Psi )$ are given by certain F-norms. As applications we consider superposition operators on some multiplier sequence spaces of Maddox type. (English) |
| Keyword:
|
sequence space |
| Keyword:
|
superposition operator |
| Keyword:
|
modulus function |
| Keyword:
|
continuity |
| MSC:
|
46A45 |
| MSC:
|
47H30 |
| idZBL:
|
Zbl 1174.47048 |
| idMR:
|
MR2356280 |
| . |
| Date available:
|
2009-09-24T11:49:25Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128206 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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