Szlenk and w*-dentability indices of the Banach spaces C([0, α])

Let α be an infinite ordinal and γ the unique ordinal satisfying ωω ^γ≤α<ωω ^γ+1. We show that the Banach space C([0, α]) of all continuous scalar-valued functions on the compact ordinal interval [0, α] has Szlenk index equal to ω ^γ+1 and w*-dentability index equal to ω ^1+γ+1.