Given a compact Hausdor® space K and a regular positive ¯nite, Borel measure ¹ on K, we characterize the operators on C(K) admitting a factorization through the natural inclusion of C(K) into L1(K; ¹). We also characterize the operators on L1(; º), with º a positive ¯nite measure, that factor through the natural inclusion of L1(; º) into L1(; º).
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