The strong WCD property for Banach spaces
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=...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
1995-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171295000081 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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. |
|---|---|
| ISSN: | 0161-1712 1687-0425 |