Abstract.
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.
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The first author was supported by the grants: Institutional Research Plan AV0Z10190503, A100190502, GA ČR 201/04/0090.
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Hájek, P., Lancien, G. Various Slicing Indices on Banach Spaces. MedJM 4, 179–190 (2007). https://doi.org/10.1007/s00009-007-0111-4
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DOI: https://doi.org/10.1007/s00009-007-0111-4