Essential norm of the difference of composition operators on Bloch space

Let ϕ and ψ be holomorphic self-maps of the unit disk, and denote by C _ϕ , C _ψ the induced composition operators. This paper gives some simple estimates of the essential norm for the difference of composition operators C _ϕ −C _ψ from Bloch spaces to Bloch spaces in the unit disk. Compactness of the difference is also characterized.