Constructing Frostman-Blaschke Products and Applications to Operators on Weighted Bergman Spaces

Authors

Pamela Gorkin, Bucknell UniversityFollow
John Akeroyd, University of Arkansas, FayettevilleFollow

Publication Date

Summer 2015

Description

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

J. Operator Theory

Volume

74

Issue

1

First Page

149

Last Page

175

Department

Mathematics

Link to Published Version

http://www.mathjournals.org/jot/2015-074-001/2015-074-001-008.html

Recommended Citation

Gorkin, Pamela and Akeroyd, John. "Constructing Frostman-Blaschke Products and Applications to Operators on Weighted Bergman Spaces." J. Operator Theory (2015) : 149-175.