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

Let α be an infinite ordinal and γ the unique ordinal satisfying ωωγ≤α<ωωγ+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 ωγ+1 and w∗-dentability index equal to ω1+γ+1.