Szlenk and w^⁎-dentability indices of C(K)

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• 作者：R.M. Causey ^{causeyrm@miamioh.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Szlenk index ; Dentability index
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：447
• 期：2
• 页码：834-845
• 全文大小：375 K

文摘

Given any compact, Hausdorff space K   and 1<p<∞$1<p<\infty$, we compute the Szlenk and w^⁎$w^{⁎}$-dentability indices of the spaces C(K)$C(K)$ and L_p(C(K))$L_p(C(K))$. We show that if K   is compact, Hausdorff, scattered, CB(K)$CB(K)$ is the Cantor–Bendixson index of K, and ξ   is the minimum ordinal such that CB(K)⩽ω^ξ$CB(K)⩽{\omega }^{\xi }$, then Sz(C(K))=ω^ξ$Sz(C(K))={\omega }^{\xi }$ and Dz(C(K))=Sz(L_p(C(K)))=ω^1+ξ$Dz(C(K))=Sz(L_p(C(K)))={\omega }^{1+\xi }$.