×

A decomposition for a class of contractions. (English) Zbl 0859.47006

Summary: A Hilbert space contraction \(T\) is the direct sum of a strongly stable contraction and an isometry whenever the strong limit of \(\{T^{*n}T^n\); \(n\geq 1\}\) is a projection. This is the case for any compact, quasinormal or cohyponormal contraction. Such a decomposition leads to a simple proof that a contraction with no proper invariant subspace is of class \({\mathcal C}_{00}\cup {\mathcal C}_{01}\cup {\mathcal C}_{10}\).

MSC:

47A45 Canonical models for contractions and nonselfadjoint linear operators
47B20 Subnormal operators, hyponormal operators, etc.
47A65 Structure theory of linear operators
PDF BibTeX XML Cite