International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 1, Pages 67-70
The strong property for Banach spaces
Department of Mathematics, Lewis Universty, Romeoville 60441, IL, USA
Received 17 June 1993
Copyright © 1995 Dave Wilkins. 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.
In this paper, we introduce weakly compact version of the weakly countably
determined () property, the strong () property. A Banach space is said to
be if there s a sequence () of weak compact subsets of such that if is
weakly compact, there is an such that . In this case, () is called a
strongly determining sequence for . We show that and that the converse does
not hold in general. In fact, is a separable space if and only if (, weak) is an -space.
Using for an example, we show how weakly compact structure theorems may be used to
construct strongly determining sequences.