Generalized interpolation in \(H^\infty\). (English) Zbl 0145.39303

If \(T\) is an operator on a Hilbert space which commutes with an operator \(S\) such that \(1 - SS^*\) has one-dimensional range and \(\lim \Vert S^{*n}f \Vert = 0\) as \(n\to\infty\) for every element \(f\) of the space, then \(T = \varphi(S)\) for some complex valued function \(\varphi(z)\) which is analytic and bounded in the unit disk.
Reviewer: James Rovnyak


47A57 Linear operator methods in interpolation, moment and extension problems
30H10 Hardy spaces
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