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

TL;DR

This paper characterizes the quasisimilarity classes of invariant subspaces for certain $C_0$ operators with multiplicity two, showing they are determined by restrictions and compressions, and provides a canonical form.

Contribution

It establishes a complete description of invariant subspaces for $C_0$ operators with multiplicity two using quasisimilarity classes and introduces a canonical form.

Findings

Quasisimilarity class of an invariant subspace is determined by restriction and compression classes.

Provides a canonical form for invariant subspaces.

Enhances understanding of structure of $C_0$ 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 $M$.