About \(b\)-weakly compact operators on Banach lattices (Q1928218)
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: About \(b\)-weakly compact operators on Banach lattices |
scientific article; zbMATH DE number 6121272
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | About \(b\)-weakly compact operators on Banach lattices |
scientific article; zbMATH DE number 6121272 |
Statements
About \(b\)-weakly compact operators on Banach lattices (English)
0 references
2 January 2013
0 references
A subset \(B\) of a Banach lattice \(E\) is called \(b\)-order bounded if it is order bounded in \(E''\) after the canonical embedding of \(E\) in \(E''\), the bidual of \(E\). An operator from \(E\) into a Banach space \(X\), \(T:E\rightarrow X\), is called \(b\)-weakly compact if \(T(B)\) is relatively weakly compact for each \(b\)-order bounded subset \(B\) of \(E\). In their main theorem, the authors give a necessary and sufficient condition under which each operator \(T:E\rightarrow X\) is \(b\)-weakly compact.
0 references
\(b\)-weakly compact operator
0 references
Banach lattice
0 references
(\(b\))-property
0 references
\(\sigma\)-Levi property
0 references
order continuous norm
0 references
KB-space
0 references
0.9016282558441162
0 references
0.8883580565452576
0 references
