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We consider the problem of classification of invariant subspaces for theclass of uniform Jordan operators. We show that given two invariant subspaces$M_1$ and $M_2$ of a uniform Jordan operator $T=S(\theta)\oplus S(\theta)\oplus\ldots$, the subspace $M_2$ belongs to the quasiaffine orbit of $M_1$ if andonly if the restrictions $T|M_1$ and $T|M_2$ are quasisimilar and thecompression $T_{M_2^\perp}$ can be injected in the compression $T_{M_1^\perp}$.Our result refines previous work on the subject by Bercovici and Smotzer.

Quasiaffine orbits of invariant subspaces for uniform Jordan operators