The Bergman space $L^2_a(\mathbb{D})$ is the closed subspace of $L^2(\mathbb{D},dA)$ consisting of analytic functions, where $dA$ is the normalized area measure on $\mathbb{D}$. For an invariant subspace $I$ denote the restriction of $M_z$to $I$. An open problem asked by K. Zhu is that when are two restriction operators $M_I$and $M_J$ are similar? In this talk, we give some sufficient conditions in a general case.

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