Title

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

Publication Date

Summer 2015

Journal

J. Operator Theory

Volume

74

Issue

1

First Page

149

Last Page

175

Abstract

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.

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