Vol. 38, No. 3, 1971

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On iterated w-sequential closure of cones

Ralph David McWilliams

Vol. 38 (1971), No. 3, 697–715

In this paper it is proved that for each countable ordinal number α 2 there exists a separable Banach space X containing a cone P such that, if JX is the canonical map of X into its bidual X∗∗, then the α-th iterated w-sequential closure Kα(JXP) of JXP 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 α, then Kβ(JWf) fails to be normclosed in W∗∗. Further, there is constructed a (non-separable) space Z containing a cone P such that if 2 β < Ω, then Kβ(JZP) fails to be norm-closed in z ∗∗.

Mathematical Subject Classification
Primary: 46B05
Published: 1 September 1971
Ralph David McWilliams