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Journal of Function Spaces
Volume 2015, Article ID 864173, 4 pages
Research Article

A Reverse Theorem on the - Continuity of the Dual Map

1Department of Mathematics and Physics, Texas A&M University Central Texas, Killeen, TX 76548, USA
2Department of Mathematics, University of Cadiz, 11519 Puerto Real, Spain

Received 9 October 2014; Accepted 22 February 2015

Academic Editor: Henryk Hudzik

Copyright © 2015 Mienie de Kock and Francisco Javier García-Pacheco. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Given a Banach space , , and , we define the set of all for which there exist two sequences and such that converges to , has a subnet -convergent to , and for all . We prove that if is separable and reflexive and enjoys the Radon-Riesz property, then is contained in the boundary of relative to . We also show that if is infinite dimensional and separable, then there exists an equivalent norm on such that the interior of relative to is contained in .