Linearization of functions.

DANIEL CARANDO; IGNACIO ZALDUENDO

MATHEMATISCHE ANNALEN

Springer

Lugar: Berlin; Año: 2004 vol. 328 p. 683 - 700

0025-5831

Given a space $\F(U)$ of functions $f:U\longrightarrow\mathbb{C}$ which are continuous, we construct another space$\F\sb{*}(U)$ and a map $e:U\longrightarrow \F\sb{*}(U)$linearizing all functions $f\in \F(U)$ (i.e. there are $L_f \in\F\sb{*}(U)'$ such that $L_f \circ e = f$). Such linearizationsare stronger than mere preduals for $\F(U)$, for example for$\F(U)=\ell_1$, linearizations correspond to preduals of $\ell_1$which are isomorphic to $c_0$. We also address the vector-valuedcase. A number of such linearizing constructions are to be foundin the literarture, mostly for certain spaces of holomorphicfunctions. The procedure presented here generalizes all thesespecial cases.