# Invariant subspaces and Hankel type operators on a Bergman space

Preprint Series # 686
Nakazi, Takahiko and Osawa, Tomoko Invariant subspaces and Hankel type operators on a Bergman space. (2005);

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## Abstract

Let$L^2=L^2(D,r dr d \theta/\pi)$ be the Lebesgue space on the open unit disk $D$ and let $L^2_a=L^2\cap Hol(D)$ be a Bergman space on $D$. In this paper,we are interested in a closed subspace $\mathcal{M}$ of $L^2$ which is invariant under the multiplication by the coordinate funcion $z$, and a Hankel type operator from $L^2_a$ to $\mathcal{M}^\bot$. In particular, we study an invariant subspace $\mathcal{M}$ such that there does not exist a finite rank Hankel type operator except a zero operator.

Item Type: Preprint 30 copies Bergman space, invariant subspace, Hankel type operator 47-xx OPERATOR THEORY 846