On weak approximation and convexification in weighted spaces of vector-valued continuous functions
1989 ◽
Vol 31
(1)
◽
pp. 59-64
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Keyword(s):
Let X be a completely regular Hausdorff space. A Nachbin family of weights is a set V of upper-semicontinuous positive functions on X such that if u, υ ∈ V then there exists w ∈ V and t > 0 so that u, υ ≤ tw. For any Hausdorff topological vector space E, the weighted space CV0(X, E) is the space of all E-valued continuous functions f on X such that υf vanishes at infinity for all υ ∈ V. CV0(X, E) is equipped with the weighted topologywv = wv(X, E) which has as a base of neighbourhoods of zero the family of all sets of the formwhere υ ∈ Vand W is a neighbourhood of zero in E. If E is the scalar field, then the space CV0(X, E) is denoted by CV0(X). The reader is referred to [4, 6, 8] for information on weighted spaces.
2000 ◽
Vol 31
(1)
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pp. 1-8
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1991 ◽
Vol 50
(1)
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pp. 98-107
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1992 ◽
Vol 53
(1)
◽
pp. 92-102
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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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1985 ◽
Vol 97
(1)
◽
pp. 137-146
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Keyword(s):
1987 ◽
Vol 29
(1)
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pp. 65-68
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1975 ◽
Vol 19
(3)
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pp. 291-300
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1987 ◽
Vol 36
(2)
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pp. 267-278