Vol. 38, No. 3, 1971

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 1  2
Online Archive
The Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
Other MSP Journals
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