Geodesic
A new class of weakly countably determined Banach spaces
K. K. Kampoukos 1   ; S. K. Mercourakis 2
1 Department of Mathematics University of Athens Panepistemiopolis 15784 Athens, Greece
2 University of Athens Department of Mathematics Panepistemiopolis 15784 Athens, Greece
Fundamenta Mathematicae, Tome 208 (2010) no. 2, pp. 155-171 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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A class of Banach spaces, countably determined in their weak topology (hence, WCD spaces) is defined and studied; we call them strongly weakly countably determined (SWCD) Banach spaces. The main results are the following: (i) A separable Banach space not containing $\ell^1 (\mathbb{N})$ is SWCD if and only if it has separable dual; thus in particular, not every separable Banach space is SWCD. (ii) If $K$ is a compact space, then the space $C(K)$ is SWCD if and only if $K$ is countable.
DOI : 10.4064/fm208-2-3
Keywords: class banach spaces countably determined their weak topology hence wcd spaces defined studied call strongly weakly countably determined swcd banach spaces main results following separable banach space containing ell mathbb swcd only has separable dual particular every separable banach space swcd compact space space swcd only countable

K. K. Kampoukos  1   ; S. K. Mercourakis  2

1 Department of Mathematics University of Athens Panepistemiopolis 15784 Athens, Greece
2 University of Athens Department of Mathematics Panepistemiopolis 15784 Athens, Greece 
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K. K. Kampoukos; S. K. Mercourakis. A new class of weakly countably determined Banach spaces. Fundamenta Mathematicae, Tome 208 (2010) no. 2, pp. 155-171. doi: 10.4064/fm208-2-3

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