# Function spaces not containing $ell {1}$

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For $\Omega$ bounded and open subset of $\mathbb{R}^{d {0}}$ and $X$ a reflexive Banach space with 1-symmetric basis, the function space $JF {X}(\Omega)$ is defined. This class of spaces includes the classical James function space. Every member of this class is separable and has non-separable dual. We provide a proof of topological nature that $JF {X}(\Omega)$ does not contain an isomorphic copy of $\ell {1}$. We also investigate the structure of these spaces and their duals.

Author: S. A. Argyros; A. Manoussakis; M. Petrakis

Source: https://archive.org/