Abstract
Theorem 1. LetX be a Banach space. (a) IfX ∗ has a closed subspace in which no normalized sequence converges weak∗ to zero, thenl 1 is isomorphic to a subspace ofX. (b) IfX ∗ contains a bounded sequence which has no weak∗ convergent subsequence, thenX contains a separable subspace whose dual is not separable.
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The second-named author was supported in part by NSF-MPS 72-04634-A03.
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Hagler, J., Johnson, W.B. On Banach spaces whose dual balls are not weak∗ sequentially compact. Israel J. Math. 28, 325–330 (1977). https://doi.org/10.1007/BF02760638
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DOI: https://doi.org/10.1007/BF02760638