Characterizations of binormal composition operators with linear fractional symbols on H²

For an analytic function φ:D→D, the composition operator C_φ is the operator on the Hardy space H² defined by C_φf = f φ for all f in H². In this paper, we give necessary and sufficient conditions for the composition operator C_φ to be binormal where the symbol φ is a linear fractional selfmap of D. Furthermore, we show that C_φ is binormal if and only if it is centered when φ is an automorphism of D or φ(z) = sz + t, |s| + |t| ≤ 1. We also characterize several properties of binormal composition operators with linear fractional symbols on H².