On the classes of hereditarily $\ell_p$ Banach spaces

Title:

On the classes of hereditarily $\ell_p$ Banach spaces

Creator:

Azimi, Parviz and Ledari, A. A.

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:6266aa89-a576-4517-addb-4f1e0b738b61
uuid:6266aa89-a576-4517-addb-4f1e0b738b61

Subject:

Banach spaces, asymptotically isometric copy of $\ell _p$, and hereditarily $\ell _p$ Banach spaces

Type:

model:article and TEXT

Format:

bez média and svazek

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 $\ell _1$.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

1001-1009

Source:

Czechoslovak Mathematical Journal | 2006 Volume:56 | Number:3

Harvested from:

CDK

Metadata only:

false