, Volume 67, Issue 2, pp 151-161
Date: 20 Apr 2010

Quasi-wandering Subspaces in the Bergman Space

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Abstract

Let \({\mathcal{B}}\) be the Bergman shift on the Bergman space \({L_a^2}\) over the open unit disk and let I be a nontrivial invariant subspace of \({L_a^2}\) . Let P I be the orthogonal projection from \({L_a^2}\) onto I. It is proved that \({P_I\mathcal{B}(L_a^2 \ominus I)}\) is not dense in I if and only if \({I \cap \mathcal{D} \ne \{0\}}\) , where \({\mathcal{D}}\) is the Dirichlet space. It is also discussed some related topics.