C(X) As A Dual Space
Canadian journal of mathematics, Tome 24 (1972) no. 3, pp. 485-491
Voir la notice de l'article provenant de la source Cambridge University Press
It is known [1] that for compact Hausdorff X, C(X) is the dual of a Banach space if and only if X is hyperstonian, that is the closure of an open set in X is again open and the carriers of normal measures in C(X)* have dense union in X. With the desiratum of proving that C(X) is always the dual of some sort of space we broaden the concept of Banach space as follows. A Banach space may be comfortably regarded as a pair (E, B) where E is a topological linear space and B is a subset of E ; the requisite property is that the Minkowski functional of B be a complete norm whose topology coincides with that of E.
Manes, E. G. C(X) As A Dual Space. Canadian journal of mathematics, Tome 24 (1972) no. 3, pp. 485-491. doi: 10.4153/CJM-1972-041-3
@article{10_4153_CJM_1972_041_3,
author = {Manes, E. G.},
title = {C(X) {As} {A} {Dual} {Space}},
journal = {Canadian journal of mathematics},
pages = {485--491},
year = {1972},
volume = {24},
number = {3},
doi = {10.4153/CJM-1972-041-3},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1972-041-3/}
}
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