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タイトルヨミ
イソウ センケイ クウカン ニ オケル カンゼン カンビセイ ニツイテ
日本語以外のタイトル
On Fully-Completeness in Topological Vector Spaces
ファイル
言語
英語
著者
城市 篤夫
内容記述(抄録等)
Let E be a separated locally convex topological vector space and E' be its dual space. E is said to be fully complete provided any linear subspace L of E' is weakly closed in E' whenever L ∩ U° is weakly closed for every neighbourhood U of zero in E. A fully complete space is also called B-complete [3]. E is said to be B_Γ-complete provided any weakly dense subspace L of E' is weakly closed in E' whenever L ∩ U°is weakly closed for every neighbourhood U of zero in E [3]. A. Persson [2] introduced the notions of t-polar and weakly t-polar spaces. They are the spaces E which are obtained by replacing the neighbourhood U by a barrel T in the above definitions of a Bcomplete and a B_Γ-complete spaces respectively.
We shall study some generalizations and some relations of these notions. We introduce new spaces, an 〓-polar and a weakly 〓-polar spaces with 〓 a set of barrels in E. These are the spaces obtained by restricting every barrel T of E to that of 〓 in the definitions of t-polar and weakly t-polar spaces. Therefore, when 〓 is the family of all absolutely convex and closed neighbourhoods of zero (resp. all barrels) in E, an 〓-polar space is a fully complete (resp. t-polar) space and a weakly 〓-polar space is a B_Γ-complete (resp. weakly t-polar) space.
掲載誌名
島根大学文理学部紀要. 理学科編
7
開始ページ
59
終了ページ
64
ISSN
03709434
発行日
1974-03-10
NCID
AN0010806X
出版者
島根大学文理学部
出版者別表記
The Faculty of Literature and Science, Shimane University
資料タイプ
紀要論文
部局
総合理工学部
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