Contraction operators quasisimilar to a unilateral shift

Abstract:

Let ${U_n}$ denote the unilaterial shift of finite multiplicity $n$. It is shown that a contraction operator $T$ is quasisimilar to ${U_n}$ if and only if $T$ is of Class ${C_1}$., the canonical isometry $V$ associated with $T$ is pure and $T$ is $n$-cyclic with analytically independent vectors. For this, the notions of operators of analytic type and analytic independence of vectors are introduced. A characterization of the cyclic vectors of the Backward Shift is also presented.