A note on connectedness of Blaschke products
Abstract
Consider the space F of all inner functions on the unit open disk under the uniform topology, which is a metric topology induced by the H∞-norm. In the present paper, a class of Blaschke products, denoted by HSC, is introduced. We prove that for each B∈HSC, B and zB belong to the same path-connected component of F. It plays an important role of a method to select a fine subsequence of zeros. As a byproduct, we obtain that each Blaschke product in HSC has an interpolating and one-component factor.
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