Mathematics > Functional Analysis
[Submitted on 18 Mar 2014]
Title:The metric geometry of the Hamming cube and applications
View PDFAbstract:The Lipschitz geometry of segments of the infinite Hamming cube is studied. Tight estimates on the distortion necessary to embed the segments into spaces of continuous functions on countable compact metric spaces are given. As an application, the first nontrivial lower bounds on the $C(K)$-distortion of important classes of separable Banach spaces, where $K$ is a countable compact space in the family $ \{ [0,\omega],[0,\omega\cdot 2],\dots, [0,\omega^2], \dots, [0,\omega^k\cdot n],\dots,[0,\omega^\omega]\}\ ,$ are obtained.
Submission history
From: Thomas B. Schlumprecht [view email][v1] Tue, 18 Mar 2014 09:01:46 UTC (19 KB)
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