## 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