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arXiv · 1210.3696

Szlenk and $w^\ast$-dentability indices of the Banach spaces $C([0,α])$

Philip A. H. Brooker
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Abstract

Let $α$ be an infinite ordinal and $γ$ the unique ordinal satisfying $ω^{ω^γ}\leq α< ω^{ω^{γ+1}}$. 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 $ω^{γ+1}$ and $w^\ast$-dentability index equal to $ω^{1+γ+1}$.

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Philip A. H. Brooker. 2012-10-13. Szlenk and $w^\ast$-dentability indices of the Banach spaces $C([0,α])$. https://arxiv.org/abs/1210.3696

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