1. On the classes of hereditarily $\ell_p$ Banach spaces
- Creator:
- Azimi, Parviz and Ledari, A. A.
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Banach spaces, asymptotically isometric copy of $\ell _p$, and hereditarily $\ell _p$ Banach spaces
- Language:
- English
- Description:
- 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 $\ell _1$.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public