Szlenk and w*-dentability indices of C(K)

الأصل · EN

Given any compact, Hausdorff space K and 1<p<∞, we compute the Szlenk and w*-dentability indices of the spaces C(K) and Lₚ(C(K)). We show that if K is compact, Hausdorff, scattered, CB(K) is the Cantor-Bendixson index of K, and ξ is the minimum ordinal such that CB(K) ωξ, then Sz(C(K))=ωξ and Dz(C(K))=Sz(Lₚ(C(K)))= ω¹⁺ξ.