Linear fractional composition operators on \(H^ 2\). (English) Zbl 0638.47027

Let \(\phi\) be an analytic function mapping the unit disk D into itself. The composition operator \(C_{\phi}\) on \(H_ 2\) is defined by \(C_{\phi}f=f\circ \phi\). In this paper the author studies such composition operators when \(\phi\) is a linear fractional transformation. For example, the author considers the computation of the adjoint and the operator norm for certain such composition operators.
Reviewer: Ch.Swartz


47B38 Linear operators on function spaces (general)
46J15 Banach algebras of differentiable or analytic functions, \(H^p\)-spaces
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