Quasisimilarity of invariant subspaces for $C_0$ operators with multiplicity two

Abstract

For an operator $T$ of class $C_0$ with multiplicity two, we show that the quasisimilarity class of an invariant subspace $M$ is determined by the quasisimilarity classes of the restriction $T|M$ and of the compression $T_{M^{\perp }}$. We also provide a canonical form for the subspace $M$.

arXiv comment16 pages. Final version. Accepted for publication in Journal of Operator Theory