Abstract. If $\phi $ is an analytic function taking the unit disk into itself then the composition operator $C_\phi $ can be defined on the Hardy space $H^p(D)$ by $C_\phi(f)=f\circ\phi $. In this work it is shown that if some power of $C_\phi $ is compact and $\phi $ has a nonzero derivative at its unique fixed point inside the disk, then $C_\phi $ is similar to $C_\psi $ if and only if the similarity can be induced by an invertible composition operator.
AMS Subject Classification
(1991): 47B38, 47B07
Keyword(s):
Composition operator
Received October 14, 1992. (Registered under 5562/2009.)
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