| Title:
|
Further properties of Azimi-Hagler Banach spaces (English) |
| Author:
|
Azimi, Parviz |
| Author:
|
Khodabakhshian, H. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
59 |
| Issue:
|
4 |
| Year:
|
2009 |
| Pages:
|
871-878 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
For the Azimi-Hagler spaces more geometric and topological properties are investigated. Any constructed space is denoted by $X_{\alpha ,p}$. We show \item {(i)} The subspace $[(e_{n_k})]$ generated by a subsequence $(e_{n_k})$ of $(e_n)$ is complemented. \item {(ii)} The identity operator from $X_{\alpha ,p}$ to $X_{\alpha ,q}$ when $p>q$ is unbounded. \item {(iii)} Every bounded linear operator on some subspace of $X_{\alpha ,p}$ is compact. It is known that if any $X_{\alpha ,p}$ is a dual space, then \item {(iv)} duals of $X_{\alpha ,1}$ spaces contain isometric copies of $\ell _{\infty }$ and their preduals contain asymptotically isometric copies of $c_0$. \item {(v)} We investigate the properties of the operators from $X_{\alpha ,p}$ spaces to their predual. (English) |
| Keyword:
|
Banach spaces |
| Keyword:
|
compact operator |
| Keyword:
|
asymptotic isometric copy of $\ell _1$ |
| MSC:
|
46B20 |
| MSC:
|
46B25 |
| MSC:
|
47L25 |
| MSC:
|
56B45 |
| idZBL:
|
Zbl 1218.47134 |
| idMR:
|
MR2563564 |
| . |
| Date available:
|
2010-07-20T15:46:01Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140523 |
| . |
| Reference:
|
[1] Azimi, P.: A new class of Banach sequence spaces.Bull. Iran. Math. Soc. 28 (2002), 57-68. Zbl 1035.46006, MR 1992259 |
| Reference:
|
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| Reference:
|
[3] Azimi, P., Hagler, J.: Example of hereditarily $\ell_p$ Banach spaces failing the Schur property.Pac. J. Math. 122 (1987), 287-297. MR 0831114, 10.2140/pjm.1986.122.287 |
| Reference:
|
[4] Chen, D.: Asymptotically isometric copy of $c_0$ and $\ell_1$ in certain Banach spaces.J. Math. Anal. Appl. 284 (2003), 618-625. MR 1998656, 10.1016/S0022-247X(03)00368-8 |
| Reference:
|
[5] Chen, S., Lin, B. L.: Dual action of asymptotically isometric copies of $\ell_p$ $(1\leq p<\infty)$ and $c_0$.Collect. Math. 48 (1997), 449-458. Zbl 0892.46014, MR 1602639 |
| Reference:
|
[6] Diestel, J.: Sequence and Series in Banach Spaces.Springer New York (1983). MR 0737004 |
| Reference:
|
[7] Dowling, P. N.: Isometric copies of $c_0$ and $\ell_{\infty}$ in duals of Banach spaces.J. Math. Anal. Appl. 244 (2000), 223-227. Zbl 0955.46011, MR 1746799, 10.1006/jmaa.2000.6714 |
| Reference:
|
[8] Lindenstrauss, J., Tzafriri, L.: Classical Banach Spaces. I. Sequence Spaces.Springer Berlin (1977). Zbl 0362.46013, MR 0500056 |
| Reference:
|
[9] Morrison, T. J.: Functional Analysis: An Introduction to Banach Space Theory.John Wiley & Sons (2001). Zbl 1005.46004, MR 1885114 |
| Reference:
|
[10] Pelczynski, A.: Projections in certain Banach spaces.Stud. Math. 19 (1960), 209-228. Zbl 0104.08503, MR 0126145, 10.4064/sm-19-2-209-228 |
| Reference:
|
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| . |
