On some problems of M. Z. Nashed on outer inverses (Q1072073)
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: On some problems of M. Z. Nashed on outer inverses |
scientific article; zbMATH DE number 3942251
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On some problems of M. Z. Nashed on outer inverses |
scientific article; zbMATH DE number 3942251 |
Statements
On some problems of M. Z. Nashed on outer inverses (English)
0 references
1986
0 references
Let X, Y be Banach spaces and let L(X,Y) consists of all linear bounded operators mapping X into Y. Main results: 1) Every \(A\in L(X,Y)\) has a bounded outer inverse, i.e. there exists a \(B\in L(Y,X)\) such that \(BAB=B.\) 2) \(A\in L(X,Y)\) has an outer inverse B such that dim BY\(=+\infty\) if and only if there exists a subspace \(X_ 0\subset X\) such that dim \(X_ 0=+\infty\), \(AX_ 0\) is complemented in Y and \(X_ 0\cap \ker A=\{0\}\).
0 references
complemented range
0 references
bounded outer inverse
0 references
0.8230989575386047
0 references
0.8040410280227661
0 references
0.7796400189399719
0 references
