ACTA issues

Composition operators with multivalent symbol

Rebecca G. Wahl

Acta Sci. Math. (Szeged) 66:3-4(2000), 755-768

Abstract. If $\varphi $ is an analytic map of the unit disk $D$ into itself, the composition operator $C_{\varphi }$ on the Hardy space $H^2(D)$ is defined by $C_{\varphi}(f) = f\circ\varphi$. For a certain class of composition operators with multivalent symbol $\varphi$, we identify a subspace of $H^2(D)$ on which $C^*_{\varphi}$ behaves like a weighted shift. We reproduce the description of the spectrum found in [Kam75] and show for this class of composition operators that the interior of the spectrum is a disk of eigenvalues of $C^*_{\varphi}$ of infinite multiplicity.

AMS Subject Classification (1991): 47B38

Received February 9, 1999. (Registered under 2766/2009.)