On a Lemma of Milutin concerning Averaging Operators in Continuous Function Spaces
نویسنده
چکیده
We show that any infinite compact Hausdorff space S is the continuous image of a totally disconnected compact Hausdorff space S', having the same topological weight as S, by a map 95 which admits a regular linear operator of averaging, i.e., a projection of norm one of C(S') onto T, the operator u: C(iS)—>• C(T) is a regular averaging operator for y if and only if « has a representation /#/(/) = Jo/(0('. *)) dx for a suitable function fl: Tx [0, 1] -> S.
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