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Let $M_{z}$ be the multiplication operator on the Bergman space and $M_{I}$denote the restriction of $M_{z}$ to an invariant subspace $I$. A questionraised by K. Zhu is that when are two restriction operators $M_{I}$ and $M_{J}$are similar? In this note, we give some sufficient conditions of this problemin a general case.

On the similarity of restriction of the operator to an invariant subspace