Abstract
Let D be the unit disk and \(A^{2}_{\alpha}(D)\,(\alpha > -1)\) be the weighted Bergman space. In this paper, we prove that the multiplication operator \(M_{{z}^{n}}\) is similar to \(\mathop \oplus \limits _{1}^{n}\) Mz on \(A^{2}_{\alpha}(D)\).
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