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, contains no subspace isomorphic to iff every bounded subset of 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 -sequential) and on relatively weakly compact sets (weak angelic).

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DOI:
https://doi.org/10.1090/S0002-9939-1987-0870799-2

Keywords:
Weakly sequentially dense,
weakly angelic

Article copyright:
© Copyright 1987
American Mathematical Society