Linearization of functions

Given a space (U) of functions f:U which are continuous, we construct another space _*(U) and a map e:U *(U) linearizing all functions f (U) (i.e. there are L_{f *}(U) such that L_f^e=f). Such linearizations are stronger than mere preduals for (U), for example for (U)=₁, linearizations correspond to preduals of ₁ which are isomorphic to c₀. We also address the vector-valued case. A number of such linearizing constructions are to be found in the literarture, mostly for certain spaces of holomorphic functions. The procedure presented here generalizes all these special cases.Mathematics Subject Classification (2000):46E10, 46G20