INVARIANT SUBSPACES AND HANKEL-TYPE OPERATORS ON A BERGMAN SPACE

Let L2 = L2(D, rdrdθ/π) be the Lebesgue space on the open unit disc D and let L2 a = L2 ∩ Hol(D) be a Bergman space on D. In this paper, we are interested in a closed subspace M of L2 which is invariant under the multiplication by the coordinate function z, and a Hankel-type operator from L2 a to M⊥. In particular, we study an invariant subspace M such that there does not exist a finite-rank Hankel-type operator except a zero operator