Sur les cones (faiblement complets) contenus dans le dual d'un espace de Banach non-reflexif
1989 ◽
Vol 39
(3)
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pp. 321-328
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Keyword(s):
Let B be a Banach space. consider the convex proper weakly complete cones X contained in B′ with σ(B′, B) such that X ∩ B′, is conic in the sense of Asimow: that is, there exists α ≥ 0 and f ∈ B″ such that ‖ ‖B ≤ f ≤ α·‖ ‖B on X. This class arises in the theory of integral representations.If B is reflexive, such a cone has a weakly-compact basis. This paper considers the converse problem:- if one requires that X ∩ B′1 be σ(B′, B) metrisable, the existence of X (without a compact σ(B′, B) basis) is equivalent to the statement that B is not a Grothendieck space.However, in every space C(K) with infinitely compact K, one can find such a cone X. If two such cones in B′ are not too far apart, their sum belongs to this class.
1993 ◽
Vol 35
(2)
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pp. 207-217
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Keyword(s):
1999 ◽
Vol 42
(2)
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pp. 139-148
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1980 ◽
Vol 32
(2)
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pp. 421-430
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Keyword(s):
1977 ◽
Vol 29
(5)
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pp. 963-970
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Keyword(s):
1976 ◽
Vol 19
(1)
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pp. 7-12
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Keyword(s):
1984 ◽
Vol 37
(3)
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pp. 358-365
Keyword(s):
Keyword(s):
1994 ◽
Vol 17
(2)
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pp. 161-171
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