| Title:
|
Barrelledness of generalized sums of normed spaces (English) |
| Author:
|
Fernández, A. |
| Author:
|
Florencio, M. |
| Author:
|
Oliveros, J. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
50 |
| Issue:
|
3 |
| Year:
|
2000 |
| Pages:
|
459-465 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $(E_{i})_{i\in I}$ be a family of normed spaces and $\lambda $ a space of scalar generalized sequences. The $\lambda $-sum of the family $(E_{i})_{i\in I}$ of spaces is \[ \lambda \lbrace (E_{i})_{i\in I}\rbrace :=\lbrace (x_{i})_{i\in I},x_{i}\in E_{i}, \quad \text{and}\quad (\Vert x_{i}\Vert )_{i\in I}\in \lambda \rbrace . \] Starting from the topology on $\lambda $ and the norm topology on each $E_i,$ a natural topology on $\lambda \lbrace (E_i)_{i\in I}\rbrace $ can be defined. We give conditions for $\lambda \lbrace (E_i)_{i\in I}\rbrace $ to be quasi-barrelled, barrelled or locally complete. (English) |
| Keyword:
|
barrelled spaces |
| Keyword:
|
generalized sequences |
| MSC:
|
46A08 |
| MSC:
|
46A45 |
| MSC:
|
46E10 |
| MSC:
|
46E40 |
| idZBL:
|
Zbl 1079.46500 |
| idMR:
|
MR1777469 |
| . |
| Date available:
|
2009-09-24T10:34:42Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127585 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
