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 $\ell _1$ 
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     author = {Azimi, Parviz and Khodabakhshian, H.},
     title = {Further properties of {Azimi-Hagler} {Banach} spaces},
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}
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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/

[1] Azimi, P.: A new class of Banach sequence spaces. Bull. Iran. Math. Soc. 28 (2002), 57-68. | MR | Zbl

[2] Azimi, P.: On geometric and topological properties of the classes of hereditarily $\ell_p$ Banach spaces. Taiwanese J. Math. 10 (2006), 713-722. | DOI | MR | Zbl

[3] Azimi, P., Hagler, J.: Example of hereditarily $\ell_p$ Banach spaces failing the Schur property. Pac. J. Math. 122 (1987), 287-297. | DOI | MR

[4] Chen, D.: Asymptotically isometric copy of $c_0$ and $\ell_1$ in certain Banach spaces. J. Math. Anal. Appl. 284 (2003), 618-625. | DOI | MR

[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. | MR | Zbl

[6] Diestel, J.: Sequence and Series in Banach Spaces. Springer New York (1983). | MR

[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. | DOI | MR | Zbl

[8] Lindenstrauss, J., Tzafriri, L.: Classical Banach Spaces. I. Sequence Spaces. Springer Berlin (1977). | MR | Zbl

[9] Morrison, T. J.: Functional Analysis: An Introduction to Banach Space Theory. John Wiley & Sons (2001). | MR | Zbl

[10] Pelczynski, A.: Projections in certain Banach spaces. Stud. Math. 19 (1960), 209-228. | DOI | MR | Zbl

[11] Popov, M. M.: More examples of hereditarily $\ell_p$ Banach spaces. Ukrainian Math. Bull. 2 (2005), 95-111. | MR | Zbl