Spaces of Continuous Vector Functions as Duals
1988 ◽
Vol 31
(1)
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pp. 70-78
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Keyword(s):
AbstractA 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.
1989 ◽
Vol 32
(1)
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pp. 98-104
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2001 ◽
Vol 70
(3)
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pp. 323-336
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Keyword(s):
1965 ◽
Vol 15
(2)
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pp. 299-304
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Keyword(s):
2002 ◽
Vol 119
(2)
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pp. 291-299
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1971 ◽
Vol 23
(3)
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pp. 468-480
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1979 ◽
Vol 31
(4)
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pp. 890-896
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