Finite rank intermediate Hankel operators and the big Hankel operator

Abstract

Let La2 be a Bergman space. We are interested in an intermediate Hankel operator HφM from La2 to a closed subspace M of L2 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 HφM is close to big Hankel operator. As a result, we give a necessary and sufficient condition about M that there does not exist a finite rank HφM except HφM=0.