C(X) As A Dual Space
1972 ◽
Vol 24
(3)
◽
pp. 485-491
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Keyword(s):
Open Set
◽
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.
1967 ◽
Vol 63
(2)
◽
pp. 311-313
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Keyword(s):
1972 ◽
Vol 72
(1)
◽
pp. 7-9
Keyword(s):
1988 ◽
Vol 11
(3)
◽
pp. 585-588
1989 ◽
Vol 106
(2)
◽
pp. 277-280
◽
1972 ◽
Vol 72
(1)
◽
pp. 37-47
◽
1969 ◽
Vol 66
(3)
◽
pp. 541-545
◽
Keyword(s):
1968 ◽
Vol 64
(2)
◽
pp. 335-340
◽
Keyword(s):
Keyword(s):
2006 ◽
Vol 2006
◽
pp. 1-7
Keyword(s):