Abstract.
In a 1988 paper, Cowen found a formula expressing the adjoint of any linear fractional composition operator on the Hardy space as a product of Toeplitz operators and another linear fractional composition operator. In this paper, we use Cowen's adjoint formula to give a unitary equivalence relating composition operators on different weighted Hardy spaces. This result is then applied to some composition operators on the S a spaces. We find the spectrum of any linear fractional composition operator whose symbol has exactly one fixed point of multiplicity one on the unit circle.
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Received: 10.5.1996
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Hurst, P. Relating composition operators on different weighted Hardy spaces. Arch. Math. 68, 503–513 (1997). https://doi.org/10.1007/s000130050083
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DOI: https://doi.org/10.1007/s000130050083