Geodesic
Further properties of Azimi-Hagler Banach spaces
Czechoslovak Mathematical Journal, Tome 59 (2009) no. 4, pp. 871-878 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 46B20, 46B25, 47L25, 56B45
Keywords: Banach spaces; compact operator; asymptotic isometric copy of $\ell _1$ 
@article{CMJ_2009_59_4_a1,
     author = {Azimi, Parviz and Khodabakhshian, H.},
     title = {Further properties of {Azimi-Hagler} {Banach} spaces},
     journal = {Czechoslovak Mathematical Journal},
     pages = {871--878},
     year = {2009},
     volume = {59},
     number = {4},
     mrnumber = {2563564},
     zbl = {1218.47134},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2009_59_4_a1/}
}
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Azimi, Parviz; Khodabakhshian, H. Further properties of Azimi-Hagler Banach spaces. Czechoslovak Mathematical Journal, Tome 59 (2009) no. 4, pp. 871-878. http://geodesic.mathdoc.fr/item/CMJ_2009_59_4_a1/