Abstract
Let V = V 0 ⊕ V 1 V = {V_0} \oplus {V_1} be an isometry, where V 0 {V_0} is unitary and V 1 {V_1} is a unilateral shift of finite multiplicity n. Let S = S 0 ⊕ S 1 S = {S_0} \oplus {S_1} be a subnormal operator where S 0 ⊕ S 1 {S_0} \oplus {S_1} is the normal decomposition of S into a normal operator S 0 {S_0} and a completely nonnormal operator S 1 {S_1} . It is shown that S is quasisimilar to V if and only if S 0 {S_0} is unitarily equivalent to V 0 {V_0} and S 1 {S_1} is quasisimilar to V 1 {V_1} . To prove this, a standard representation is developed for n-cyclic subnormal operators. Using this representation, the class of subnormal operators which are quasisimilar to V 1 {V_1} is completely characterized.
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