On Banach spaces whose dual balls are not weak∗ sequentially compact
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Theorem 1. Let X be a Banach space. (a) If X * has a closed subspace in which no normalized sequence converges weak* to zero, then l 1 is isomorphic to a subspace of X. (b) If X * contains a bounded sequence which has no weak* convergent subsequence, then X contains a separable subspace whose dual is not separable. © 1997 The Weizmann Science Press of Israel.
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Hagler, J., & Johnson, W. B.
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