Geodesic
Spaces of Continuous Vector Functions as Duals
Canadian mathematical bulletin, Tome 31 (1988) no. 1, pp. 70-78

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DOI

A well known result due to Dixmier and Grothendieck for spaces of continuous scalar-valued functions C(X), X compact Hausdorff, is that C(X) is a Banach dual if, and only if, Xis hyperstonean. Moreover, for hyperstonean X, the predual of C(X) is strongly unique. Here we obtain a formulation of this result for spaces of continuous vector-valued functions. It is shown that if E is a Hilbert space and C(X, (E, σ *) ) denotes the space of continuous functions on X to E when E is provided with its weak * ( = weak) topology, then C(X, (E, σ *) ) is a Banach dual if, and only if, X is hyperstonean. Moreover, for hyperstonean X, the predual of C(X, (E, σ *) ) is strongly unique.
DOI : 10.4153/CMB-1988-011-3
Mots-clés : 46E40, 46E15, 46G10 
Cambern, Michael; Greim, Peter. Spaces of Continuous Vector Functions as Duals. Canadian mathematical bulletin, Tome 31 (1988) no. 1, pp. 70-78. doi: 10.4153/CMB-1988-011-3
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     author = {Cambern, Michael and Greim, Peter},
     title = {Spaces of {Continuous} {Vector} {Functions} as {Duals}},
     journal = {Canadian mathematical bulletin},
     pages = {70--78},
     year = {1988},
     volume = {31},
     number = {1},
     doi = {10.4153/CMB-1988-011-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1988-011-3/}
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