Various Slicing Indices on Banach Spaces

We give a short and direct proof for the computation of the Szlenk index of the C(K) spaces, when K is a countable compact space and determine their Lavrientiev indices. We also compute the Szlenk index of certain C(α) spaces, where α is an uncountable ordinal. Finally, we show that if the Szlenk index of a Banach space is ω (first infinite ordinal), then its weak*-dentability index is at most ω² and that this estimate is optimal. The first author was supported by the grants: Institutional Research Plan AV0Z10190503, A100190502, GA ČR 201/04/0090.