Quasiaffine orbits of invariant subspaces for uniform Jordan operators

Raphaël Clouâtre

paper

Quasiaffine orbits of invariant subspaces for uniform Jordan operators

arXiv:1108.5480

Abstract

We consider the problem of classification of invariant subspaces for the class of uniform Jordan operators. We show that given two invariant subspaces $M_{1}$ and $M_{2}$ of a uniform Jordan operator $T = S (θ) \oplus S (θ) \oplus \dots$ , the subspace $M_{2}$ belongs to the quasiaffine orbit of $M_{1}$ if and only if the restrictions $T ∣ M_{1}$ and $T ∣ M_{2}$ are quasisimilar and the compression $T_{M_{2}^{⊥}}$ can be injected in the compression $T_{M_{1}^{⊥}}$ . Our result refines previous work on the subject by Bercovici and Smotzer.

arXiv comment11 pages. Final version. Accepted for publication in Journal of Functional Analysis