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KMID : 0368019830060020237
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Journal of Soonchunhyang University
1983 Volume.6 No. 2 p.237 ~ p.241
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On Some Properties in Barrelled Spaces
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Kim Byung-Young
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Abstract
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Theorem 1. LetXbe´lcs(DF) space. Then the following conditions are equivalent
(a) X is co barrelled
(b) X is C barrelled
(c,) X is sequentially barrelled (d) X is Banach-Mackey space
Theorem 2. If X is relatively strong. Then X is C barrelled if and only if (X f, weak*) is
sequentially complete.
Theorem 3. Let X be a lcs relatively strong and Mazur. Then the following statements are equivalent.
(a) X is sequentially barrelled
(b) X is Banach-Mackey space
(c) (X´, weak*) is sequentially complete
(d) (X´, Mackey*) is sequentially complete
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