Metric entropy of convex hulls in Hilbert spaces
Li, Wenbo ; Linde, Werner
Studia Mathematica, Tome 141 (2000), p. 29-45 / Harvested from The Polish Digital Mathematics Library
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Let T be a precompact subset of a Hilbert space. We estimate the metric entropy of co(T), the convex hull of T, by quantities originating in the theory of majorizing measures. In a similar way, estimates of the Gelfand width are provided. As an application we get upper bounds for the entropy of co(T), T=t1,t2,..., ||tj||≤aj, by functions of the aj’s only. This partially answers a question raised by K. Ball and A. Pajor (cf. [1]). Our estimates turn out to be optimal in the case of slowly decreasing sequences (aj)j=1∞.

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:216709 
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Li, Wenbo; Linde, Werner. Metric entropy of convex hulls in Hilbert spaces. Studia Mathematica, Tome 141 (2000) pp. 29-45. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv139i1p29bwm/

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