Geodesic
Uniqueness of Preduals for Spaces of Continuous Vector Functions
Canadian mathematical bulletin, Tome 32 (1989) no. 1, pp. 98-104

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A. Grothendieck has shown that if the space C(X) is a Banach dual then X is hyperstonean; moreover, the predual of C(X) is strongly unique. In this article we give a vector analogue of Grothendieck's result. We show that if E* is a reflexive Banach 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 the full content of Grothendieck's theorem for C(X) can be established for C(X,(E*,σ*)). This improves a result previously obtained for the case in which E* is Hilbert space. 
Cambern, Michael; Greim, Peter. Uniqueness of Preduals for Spaces of Continuous Vector Functions. Canadian mathematical bulletin, Tome 32 (1989) no. 1, pp. 98-104. doi: 10.4153/CMB-1989-014-0
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     author = {Cambern, Michael and Greim, Peter},
     title = {Uniqueness of {Preduals} for {Spaces} of {Continuous} {Vector} {Functions}},
     journal = {Canadian mathematical bulletin},
     pages = {98--104},
     year = {1989},
     volume = {32},
     number = {1},
     doi = {10.4153/CMB-1989-014-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1989-014-0/}
}
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