A projection property and weak sequential completeness of \(\alpha\)-duals (Q685931)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: A projection property and weak sequential completeness of \(\alpha\)-duals |
scientific article; zbMATH DE number 425609
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A projection property and weak sequential completeness of \(\alpha\)-duals |
scientific article; zbMATH DE number 425609 |
Statements
A projection property and weak sequential completeness of \(\alpha\)-duals (English)
0 references
18 October 1993
0 references
A theorem of G. Bennett states that the \(\alpha\)-dual, \(E^ \alpha\), of a monotone sequence space \(E\) containing the space of sequences with finite support is \(\sigma(E^ \alpha,E)\)-sequentially complete. In this paper, we show that the Hahn-Schur theorem for summability can be used to give a generalization of Bennett's result to a wider class of sequence spaces than the monotone spaces. The methods employed are also applicable to vector-valued sequence spaces.
0 references
weak sequential completeness
0 references
\(\alpha\)-dual
0 references
sequentially
0 references
monotone sequence space
0 references
Hahn-Schur theorem
0 references
vector-valued sequence spaces
0 references
