| Title:
|
Sequentially Right Banach spaces of order $p$ (English) |
| Author:
|
Dehghani, Mahdi |
| Author:
|
Dehghani, Mohammad B. |
| Author:
|
Moshtaghioun, Mohammad S. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
61 |
| Issue:
|
1 |
| Year:
|
2020 |
| Pages:
|
51-67 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We introduce and study two new classes of Banach spaces, the so-called sequentially Right Banach spaces of order $p$, and those defined by the dual property, the sequentially Right$^*$ Banach spaces of order $p$ for $1\leq p\leq\infty$. These classes of Banach spaces are characterized by the notions of $L_p$-limited sets in the corresponding dual space and $R^*_p$ subsets of the involved Banach space, respectively. In particular, we investigate whether the injective tensor product of a Banach space $X$ and a reflexive Banach space $Y$ has the sequentially Right property of order $p$ when $X$ enjoys this property. (English) |
| Keyword:
|
Right topology |
| Keyword:
|
sequentially Right Banach space |
| Keyword:
|
pseudo weakly compact operator |
| Keyword:
|
Pełczyński's property (V) of order $p$ |
| Keyword:
|
limited $p$-converging operator |
| Keyword:
|
$p$-Gelfand--Phillips property |
| Keyword:
|
reciprocal Dunford--Pettis property of order $p$ |
| MSC:
|
46B20 |
| MSC:
|
46B25 |
| MSC:
|
47L05 |
| idZBL:
|
Zbl 07217158 |
| idMR:
|
MR4093429 |
| DOI:
|
10.14712/1213-7243.2020.011 |
| . |
| Date available:
|
2020-04-30T11:17:22Z |
| Last updated:
|
2022-04-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148075 |
| . |
| Reference:
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