On the distortion of a linear embedding of C(K) into a C0(Γ,X) space

In this paper we study the distortion ‖T‖‖T−1‖ of a linear embedding T:C(K)→C0(Γ,X) where K is a Hausdorff compactum and Γ is an infinite discrete space. We prove that if X has no subspace isomorphic to c0 and if for some n<ω the nth derivative of K is non-empty, then ‖T‖‖T−1‖≥2n+1. This result extends a previous result from [3] and answers an open question from [4].