small Hankel operator. L2 has the following orthogonal decomposition:

from L2a 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 HMφ 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 HMφ except H M φ = 0