Contractibility of compact contractions in Hilbert space (Q5957208)
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: Contractibility of compact contractions in Hilbert space |
scientific article; zbMATH DE number 1716590
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Contractibility of compact contractions in Hilbert space |
scientific article; zbMATH DE number 1716590 |
Statements
Contractibility of compact contractions in Hilbert space (English)
0 references
28 November 2002
0 references
Hilbert space
0 references
spectral radius
0 references
contraction
0 references
compact operator
0 references
0 references
A necessary and sufficient condition for the spectral radius of a compact contraction being less than one is stated. NEWLINENEWLINENEWLINELet \(\Sigma\) denote a finite set of compact contractions on a complex Hilbert space. Then the spectral radius of \(A\) is less than one for all \(A\) in the multiplicative semigroup generated by \(\Sigma\) if and only if there exists a positive integer \(N\) such that norm of \(A\) is less than one for all \(A\) in the set of all products of operators in \(\Sigma\) of length \(N\). NEWLINENEWLINENEWLINERelated extensions and examples are considered.
0 references
