Characterizations of binormal composition operators with linear fractional symbols on H-2

Abstract

For an analytic function to phi : D > D, the composition operator C-phi is the operator on the Hardy space H-2 defined by C(phi)f = f . phi to for all f in H-2. In this paper, we give necessary and sufficient conditions for the composition operator C-phi to be binorrnal where the symbol phi is a linear fractional selfmap of D. Furthermore, we show that C-phi is binormal if and only if it is centered when //) is an automorphism of D or phi(z) = sz + t, \s\ + \t\ <= 1. We also characterize several properties of binormal composition operators with linear fractional symbols on H-2. (C) 2015 Elsevier Inc. All rights reserved.