Open decompositions on ordered convex spaces
1973 ◽
Vol 74
(1)
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pp. 49-59
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Keyword(s):
Let (E, ) be a topological vector space with a positive cone C. Jameson (3) says that C given an open decomposition on E if V ∩ C − V ∩ C is a -neighbourhood of 0 whenever V is a -neighbourhood of 0. The concept of open decompositions plays an important rôle in the theory of ordered topological vector spaces; see (3). It is clear that C is generating if C gives an open decomposition on E; the converse is true for Banach spaces with a closed cone, by Andô's theorem (cf. (1) or (9)). Therefore the following question arises naturally:(Q 1) Let (E, ) be a locally convex space with a positive cone C. What condition on is necessary and sufficient for the cone C to give an open decomposition on E?
1971 ◽
Vol 14
(1)
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pp. 119-120
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2011 ◽
Vol 49
(1)
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pp. 89-98
Keyword(s):
1987 ◽
Vol 43
(2)
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pp. 224-230
1956 ◽
Vol 3
(1)
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pp. 9-12
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Keyword(s):
1979 ◽
Vol 22
(1)
◽
pp. 35-41
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Keyword(s):
1980 ◽
Vol 32
(2)
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pp. 460-479
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1982 ◽
Vol 34
(2)
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pp. 406-410
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