Separation for Kernels of Hankel Operators
by
Caixing Gu
California Polytechnic State University

We prove that for two Hankel operators H_a1 and H_a2 on the Hardy space of the unit disk either the kernel of H_a1^*H_a2 equals the kernel of H_a2 or the kernel of H_a2^*H_a1 equals the kernel of H_a1. In fact we prove a version of the above result for products of an arbitrary finite number of Hankel operators. Some immediate corollaries are generalizations the result of Brown and Halmos on zero products of two Hankel operators and the result of Axler, Chang and Sarason on finite rank products of two Hankel operators. Simple examples show our results are sharp.

Date received: May 4, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacb-40.