Estimating the gap of finite metric spaces of strict p-negative type

Let (X,d) be a finite metric space. This paper first discusses the spectrum of the p-distance matrix of a finite metric space of p-negative type and then gives upper and lower bounds for the so called gap Γ(X,p) of a finite metric space of strict p-negative type. Furthermore estimations for Γ(X,p) under a certain gluing construction for finite metric spaces are given and finally be applied to finite ultrametric spaces.