p. 153 - 160 On the dual space
C_{0}^{*}(S, X) L. Meziani Received: April 9, 2008;
Revised: September 24, 2008;
Accepted: September 26, 2008
Abstract.
Let S be a locally compact Hausdorff space and let us consider the space
C_{0}(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 C_{0}^{*}(S, X)
is isometrically isomorphic to the Banach space
rσbv(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.
Keywords:
vector-valued functions; bounded functionals; vector measures.
AMS Subject classification:
Primary: 46E40;
Secondary: 46G10.
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