Abstract of a paper by S.A. Argyros, A. Manoussakis, and M. Petrakis
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
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