Finite rank intermediate Hankel operators and the big Hankel operator

Let La be a Bergman space. We are interested in an intermediate Hankel operator H M φ from La to a closed subspace M of L 2 which is invariant under the multiplication by the coordinate function z. It is well known that there do not exist any nonzero finite rank big Hankel operators, but we are studying same types in case H φ is close to big Hankel operator. As a result, we give a necessary and sufficient condition aboutM that there does not exist a finite rank H φ except H M φ = 0.