On the classes of hereditarily $\ell_p$ Banach spaces

Azimi, P. ; Ledari, A. A.

Czechoslovak Mathematical Journal, Tome 56 (2006) no. 3, pp. 1001-1009.

Résumé

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 $\ell _1$.

Détail

Classification : 46B04, 46B20, 46B25
Mots-clés : Banach spaces; asymptotically isometric copy of $\ell _p$; hereditarily $\ell _p$ Banach spaces