Geodesic
On the classes of hereditarily $\ell_p$ Banach spaces
Czechoslovak Mathematical Journal, Tome 56 (2006) no. 3, pp. 1001-1009 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Let $X$ denote a specific space of the class of $X_{\alpha ,p}$ Banach sequence spaces which were constructed by Hagler and the first named author as classes of hereditarily $\ell _p$ Banach spaces. We show that for $p>1$ the Banach space $X$ contains asymptotically isometric copies of $\ell _{p}$. It is known that any member of the class is a dual space. We show that the predual of $X$ contains isometric copies of $\ell _q$ where $\frac{1}{p}+\frac{1}{q}=1$. For $p=1$ it is known that the predual of the Banach space $X$ contains asymptotically isometric copies of $c_0$. Here we give a direct proof of the known result that $X$ contains asymptotically isometric copies of $\ell _1$.
Let $X$ denote a specific space of the class of $X_{\alpha ,p}$ Banach sequence spaces which were constructed by Hagler and the first named author as classes of hereditarily $\ell _p$ Banach spaces. We show that for $p>1$ the Banach space $X$ contains asymptotically isometric copies of $\ell _{p}$. It is known that any member of the class is a dual space. We show that the predual of $X$ contains isometric copies of $\ell _q$ where $\frac{1}{p}+\frac{1}{q}=1$. For $p=1$ it is known that the predual of the Banach space $X$ contains asymptotically isometric copies of $c_0$. Here we give a direct proof of the known result that $X$ contains asymptotically isometric copies of $\ell _1$.
Classification : 46B04, 46B20, 46B25
Keywords: Banach spaces; asymptotically isometric copy of $\ell _p$; hereditarily $\ell _p$ Banach spaces 
@article{CMJ_2006_56_3_a18,
     author = {Azimi, P. and Ledari, A. A.},
     title = {On the classes of hereditarily $\ell_p$ {Banach} spaces},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1001--1009},
     year = {2006},
     volume = {56},
     number = {3},
     mrnumber = {2261672},
     zbl = {1164.46304},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2006_56_3_a18/}
}
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Azimi, P.; Ledari, A. A. On the classes of hereditarily $\ell_p$ Banach spaces. Czechoslovak Mathematical Journal, Tome 56 (2006) no. 3, pp. 1001-1009. http://geodesic.mathdoc.fr/item/CMJ_2006_56_3_a18/