Abstract. A necessary condition will be given for the hyponormality of $C^*_\phi $ when $\phi $ is a linear fractional transformation mapping the unit disk into itself. This necessary condition is an improvement on a condition given by Sadraoui and partially answers a question raised by Cowen and MacCluer.

AMS Subject Classification (1991): 47B20, 47B33

Keyword(s): Composition Operators, Hyponormality

Received October 27, 2000, and in revised form July 5, 2001. (Registered under 2848/2009.)