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Entropy of C(K)-Valued Operators

✍ Scribed by Ingo Steinwart

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
252 KB
Volume
103
Category
Article
ISSN
0021-9045

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✦ Synopsis

We investigate how the entropy numbers (e n (T )) of an arbitrary Ho lder-continuous operator T: E Γ„ C(K ) are influenced by the entropy numbers (= n (K )) of the underlying compact metric space K and the geometry of E. We derive diverse universal inequalities relating finitely many = n (K )'s with finitely many e n (T )'s which yield statements about the asymptotically optimal behaviour of the sequence (e n (T )) in terms of the sequence (= n (K )). As an application we present new methods for estimating the entropy numbers of a precompact and convex subset in a Banach space E, provided that the entropy numbers of its extremal points are known.

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