Weak sequential denseness in Banach spaces

Howard, J.

doi:10.1090/S0002-9939-1987-0870799-2

Weak sequential denseness in Banach spaces
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by J. Howard PDF

Proc. Amer. Math. Soc. 99 (1987), 351-352 Request permission

Corrigendum: Proc. Amer. Math. Soc. 104 (1988), 334.

Abstract:

H. P. Rosenthal [Some recent discoveries in the isomorphic theory of Banach spaces, Bull. Amer. Math. Soc. 84 (1978), 803-831] has shown that for separable Banach spaces, $X$ contains no subspace isomorphic to ${l_1}$ iff every bounded subset of $X$ is weakly sequentially dense in its weak closure (bwsd property). We show this is true for Banach spaces in general and compare the bwsd property to weak sequential denseness on arbitrary sets (weak $N$-sequential) and on relatively weakly compact sets (weak angelic).

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