International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 51705, 3 pages

Finite rank intermediate Hankel operators and the big Hankel operator

Tomoko Osawa

Mathematical and Scientific Subjects, Asahikawa National College of Technology, Asahikawa 071-8142, Japan

Received 28 March 2006; Accepted 28 March 2006

Copyright © 2006 Tomoko Osawa. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.