Characterizations of binormal composition operators with linear fractional symbols on H2

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