Hyponormal powers of composition operators


Let Ti, i = 1, 2, be measurable transformations which define bounded composition operators CTi on L2 of a σ-finite measure space. Denote their respective Radon-Nikodym derivatives by hi, i = 1, 2. The main result of this paper is that if hi ○ Ti < h j, i, j = 1, 2, then for each of the positive integers m, n, p the operator [CTm, CT2n]p is hyponormal. As a consequence, we see that the sufficient condition established by Harrington and Whitley for hyponormality of a composition operator is actually sufficient for all powers to be hyponormal. © 1988 American Mathematical Society.

Publication Title

Proceedings of the American Mathematical Society