Toeplitz operators in the commutant of a composition operator

Abstract

If ϕ is an analytic self-mapping of the unit disc D and if $H^2(D)$ is the Hardy-Hilbert space on D, the composition operator $C_ϕ$ on $H^{2}(D)$ is defined by $C_ϕ(f) = f∘ϕ$. In this article, we consider which Toeplitz operators $T_f$ satisfy $T_{f}C_{ϕ}