An observation about Frostman shifts (Q2467664)

Let \(B(z)\) be an inner function. For \(a\in D\) denote \(B_a(z)= (B-a)/(1-\overline a B)\) a Frostman shift of \(B\). It is shown that following assertions are equivalent: 1) \(B\) is a Frostman Blaschke product; 2) \(B_a\) is a Frostman Blaschke product for some \(a\in D\); 3) \(B_a\) is a Frostman Blaschke product for all \(a\in D\).