%0 Journal Article
%T On the dual space C0*(S, X)
%A L. Meziani
%J ACTA MATHEMATICA 
UNIVERSITATIS COMENIANAE
%D 2012
%I Acta Mathematica Universitatis Comenianae
%X . Let S be a locally compact Hausdorff space and let us consider the space C0(S, X) of continuous functions vanishing at infinity, from S into the Banach space X. A theorem of I. Singer, settled for S compact, states that the topological dual C0*(S, X) is isometrically isomorphic to the Banach space r¦Òbv(S, X*) of all regular vector measures of bounded variation on S, with values in the strong dual X*. Using the Riesz-Kakutani theorem and some routine topological arguments, we propose a constructive detailed proof which is, as far as we know, different from that supplied elsewhere.
%K vector-valued functions
%K bounded functionals
%K vector measures.
%U http://www.emis.de/journals/AMUC/_vol-78/_no_1/_meziani/meziani.html