On the dual space <i>C</i><sub>0</sub><sup>*</sup>(<i>S, X</i>)
Title:
On the dual space <i>C</i><sub>0</sub><sup>*</sup>(<i>S, X</i>)
Author:
L. Meziani
Appeared in:
Acta mathematica Universitatis Comenianae
Paging:
Volume LXXVIII (2009) nr. 1 pages 153-160
Year:
2009
Contents:
Let <i>S</i> be a locally compact Hausdorff space and let us consider the space <i>C</i><sub>0</sub>(<i>S, X</i>) of continuous functions vanishing at infinity, from <i>S</i> into the Banach space <i>X</i>. A theorem of I. Singer, settled for <i>S</i> compact, states that the topological dual <i>C</i><sub>0</sub><sup>*</sup>(<i>S, X</i>) is isometrically isomorphic to the Banach space <i>r</i>σ<i>bv</i>(<i>S, X</i><sup>*</sup>) of all regular vector measures of bounded variation on <i>S</i>, with values in the strong dual <i>X</i><sup>*</sup>. 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.
Publisher:
Acta Mathematica Universitatis Comenianae (provided by DOAJ)
Journal description