This is an announcement for the paper "Function spaces not containing $\ell_{1}$" by S.A. Argyros, A. Manoussakis, and M. Petrakis.

Abstract: 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.

Archive classification: math.FA

Mathematics Subject Classification: 46B10

Citation: Israel Journal of Mathematics 135 (2003), 29-81

Submitted from: amanousakis@isc.tuc.gr

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1210.2379

or

http://arXiv.org/abs/1210.2379