The strong WCD property for Banach spaces

Autor: Dave Wilkins
Jazyk: angličtina
Rok vydání: 1995
Předmět:
Zdroj: International Journal of Mathematics and Mathematical Sciences, Vol 18, Iss 1, Pp 67-70 (1995)
Druh dokumentu: article
ISSN: 0161-1712
1687-0425
01611712
DOI: 10.1155/S0161171295000081
Popis: 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 K⊂X is weakly compact, there is an (nm)⊂N such that K⊂⋂m=1∞Anm⊂X. In this case, (An) is called a strongly determining sequence for X. We show that SWCG⇒SWCD 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 ℵ0-space. Using c0 for an example, we show how weakly compact structure theorems may be used to construct strongly determining sequences.
Databáze: Directory of Open Access Journals
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