Constructing Frostman-Blaschke Products and Applications to Operators on Weighted Bergman Spaces
We give an example of a uniform Frostman-Blaschke product B, whose spectrum is a Cantor set, such that the composition operator C-B is not closed-range on any weighted Bergman space A(alpha)(p), answering two questions posed in recent papers. We include some general observations about these Blaschke products. Using methods developed in our first example, we improve upon a theorem of V.I. Vasjunin concerning the rate at which the zeros of a uniform Frostman-Blaschke product approach the unit circle.
Journal of Operator Theory
Akeroyd, John R. and Gorkin, Pamela. "Constructing Frostman-Blaschke Products and Applications to Operators on Weighted Bergman Spaces." Journal of Operator Theory (2015) : 149-175.