Subspaces with property (b) in locally convex spaces of quasi-barrelled type
1980 ◽
Vol 88
(2)
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pp. 331-337
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Keyword(s):
A subspace G of a locally convex space E has property (b) if for every bounded set B of E the codimension of G in the linear hull of G ∪ B is finite, (5). Extending the results of (5) and (14), we prove that, if the strong dual of E is complete, then subspaces with property (b) inherit the following properties of E: σ-evaluability, evaluability, the property of being Mazur, semibornological and bornological. We also prove that a dense subspace with property (b) of a Mazur space is sequentially dense, and of a semibornological space – dense in the sense of Mackey (locally dense, following M. Valdivia).
2020 ◽
pp. 2050027
Keyword(s):
1981 ◽
Vol 24
(3)
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pp. 369-371
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Keyword(s):
1985 ◽
Vol 28
(2)
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pp. 207-215
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Keyword(s):
2002 ◽
Vol 15
(2)
◽
pp. 91-103
Keyword(s):
1967 ◽
Vol 15
(4)
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pp. 295-296
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Keyword(s):
1985 ◽
Vol 31
(3)
◽
pp. 451-462
Keyword(s):
1983 ◽
Vol 27
(2)
◽
pp. 269-283
2014 ◽
Vol 57
(4)
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pp. 803-809
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Keyword(s):