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International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 1, Pages 67-70

The strong WCD property for Banach spaces

Department of Mathematics, Lewis Universty, Romeoville 60441, IL, USA

Received 17 June 1993

Copyright © 1995 Hindawi Publishing Corporation. 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 (WCD) property, the strong WCD (SWCD) property. A Banach space X is said to be SWCD if there s a sequence (An) of weak compact subsets of X such that if KX is weakly compact, there is an (nm)N such that Km=1AnmX. In this case, (An) is called a strongly determining sequence for X. We show that SWCGSWCD and that the converse does not hold in general. In fact, X is a separable SWCD space if and only if (X, weak) is an 0-space. Using c0 for an example, we show how weakly compact structure theorems may be used to construct strongly determining sequences.