On iteratedw∗-sequential closure of cones
R. D. McWilliams · Pacific Journal of Mathematics · 1971
In this paper it is proved that for each countable ordinal number a ^ 2 there exists a separable Banach space X containing a cone P such that, if J x is the canonical map of X into its bidual X**, then the αth iterated w*-sequential closure K a (J x P) of J X P fails to be norm-closed in X**.From such spaces there is constructed a separable space W containing a cone P such that if 2 ^ β ^ a, then Kβ{J w P) fails to be normclosed in FT**.Further, there is constructed a (non-separable) space Z containing a cone P such that if 2 S β < Ω, then Kβ(J z P) fails to be norm-closed in Z**.