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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Weak sequential denseness in Banach spaces


Author: J. Howard
Journal: Proc. Amer. Math. Soc. 99 (1987), 351-352
MSC: Primary 46B20
Corrigendum: Proc. Amer. Math. Soc. 104 (1988), 334.
MathSciNet review: 870799
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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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DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0870799-2
PII: S 0002-9939(1987)0870799-2
Keywords: Weakly sequentially dense, weakly angelic
Article copyright: © Copyright 1987 American Mathematical Society