Common invariant subspaces for finitely quasinilpotent collections of positive operators on a Banach space with a Schauder basis (Q2478017)
From MaRDI portal
scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Common invariant subspaces for finitely quasinilpotent collections of positive operators on a Banach space with a Schauder basis |
scientific article |
Statements
Common invariant subspaces for finitely quasinilpotent collections of positive operators on a Banach space with a Schauder basis (English)
0 references
14 March 2008
0 references
The author proves that, if \(C\) is a nonempty collection of continuous positive operators on a Banach space \(X\) with a Schauder basis \(\{e_{n}\}\) that is finitely quasinilpotent at a nonzero positive vector \(x_{0}\in X\), then \(C\) and its positive commutant have a common nontrivial invariant closed subspace.
0 references
Banach spaces
0 references
Schauder basis
0 references
quasinilpotent operators
0 references
positive operators
0 references
common invariant subspaces
0 references
positive commutant
0 references
