RELATING COMPOSITION OPERATORS ON DIFFERENT WEIGHTED HARDY-SPACES

In a 1988 paper, Cowen found a formula expressing the adjoint of any l inear fractional composition operator on the Hardy space as a product of Toeplitz operators and another linear fractional composition operat or. In this paper, we use Cowen's adjoint formula to give a unitary eq uivalence relating composition operators on different weighted Hardy s paces. This result is then applied to some composition operators on th e S-a spaces. We find the spectrum of any linear fractional compositio n operator whose symbol has exactly one fixed point of multiplicity on e on the unit circle.