| Title:
|
A class of Banach sequence spaces analogous to the space of Popov (English) |
| Author:
|
Azimi, P. |
| Author:
|
Ledari, A. A. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
59 |
| Issue:
|
3 |
| Year:
|
2009 |
| Pages:
|
573-582 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Hagler and the first named author introduced a class of hereditarily $l_1$ Banach spaces which do not possess the Schur property. Then the first author extended these spaces to a class of hereditarily $l_p$ Banach spaces for $1\leq p<\infty $. Here we use these spaces to introduce a new class of hereditarily $l_p(c_0)$ Banach spaces analogous of the space of Popov. In particular, for $p=1$ the spaces are further examples of hereditarily $l_1$ Banach spaces failing the Schur property. (English) |
| Keyword:
|
Banach spaces |
| Keyword:
|
Schur property |
| Keyword:
|
hereditarily $l_p$ |
| MSC:
|
46B20 |
| MSC:
|
46B25 |
| MSC:
|
46B45 |
| MSC:
|
46E30 |
| idZBL:
|
Zbl 1224.46017 |
| idMR:
|
MR2545640 |
| . |
| Date available:
|
2010-07-20T15:26:26Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140499 |
| . |
| Reference:
|
[1] Azimi, P.: A new class of Banach sequence spaces.Bull. of Iranian Math. Society 28 (2002), 57-68. Zbl 1035.46006, MR 1992259 |
| Reference:
|
[2] Azimi, P., Hagler, J.: Examples of hereditarily $ \ell_1$ Banach spaces failing the Schur property.Pacific J. Math. 122 (1986), 287-297. MR 0831114, 10.2140/pjm.1986.122.287 |
| Reference:
|
[3] Bourgain, J.: $\ell_1$-subspace of Banach spaces.Lecture notes. Free University of Brussels. |
| Reference:
|
[4] Lindenstrauss, J., Tzafriri, L.: Classical Banach Spaces.Vol. I sequence Spaces, Springer Verlag, Berlin. Zbl 0852.46015, MR 0415253 |
| Reference:
|
[5] Popov, M. M.: A hereditarily $\ell_1$ subspace of $L_1$ without the Schur property.Proc. Amer. Math. Soc. 133 (2005), 2023-2028. Zbl 1080.46007, MR 2137868, 10.1090/S0002-9939-05-07758-0 |
| Reference:
|
[6] Popov, M. M.: More examples of hereditarily $\ell _p$ Banach spaces.Ukrainian Math. Bull. 2 (2005), 95-111. Zbl 1166.46304, MR 2172327 |
| . |
