Entropy of C(K)-Valued Operators
We investigate how the entropy numbers (e"n(T)) of an arbitrary Holder-continuous operator T:E->C(K) are influenced by the entropy numbers (@e"n(K)) of the underlying compact metric space K and the geometry of E. We derive diverse universal inequalities relating finitely many @e"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 (@e"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.