On the equivalence of composition operators
Abstract
If $\phi$ is an analytic function taking the unit disk $D$ into itself then the composition operator $C\sb{\phi}$ can be defined on the Hardy space $H\sp p(D)$ by $C\sb{\phi}(f)$ = $f \circ \phi$. In this work, the question of when two of these operators are equivalent in some sense is studied. In some cases, it turns out that the only equivalences are those that are induced by an invertible composition operator. Most notable is the case of certain compact or power compact composition operators. However, other cases are exhibited in which there are equivalences that are not induced by an invertible composition operator.
Degree
Ph.D.
Advisors
Cowen, Purdue University.
Subject Area
Mathematics
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