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

Abstract

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*-den