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  1. 紀要
  2. お茶の水女子大學自然科學報告
  3. 11(1)

Locally Convex Spaces with the Extension Property

http://hdl.handle.net/10083/2082
http://hdl.handle.net/10083/2082
904a05a2-98d3-4f01-8f95-67b76161a2af
名前 / ファイル ライセンス アクション
KJ00004829511.pdf KJ00004829511.pdf (611.0 kB)
Item type 紀要論文 / Departmental Bulletin Paper(1)
公開日 2008-04-30
タイトル
タイトル Locally Convex Spaces with the Extension Property
言語
言語 eng
資源タイプ
資源 http://purl.org/coar/resource_type/c_6501
タイプ departmental bulletin paper
著者 Sawashima, Ikuko

× Sawashima, Ikuko

WEKO 69512

Sawashima, Ikuko

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沢島, 侑子

× 沢島, 侑子

WEKO 69514

en 沢島, 侑子

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著者(ヨミ)
識別子Scheme WEKO
識別子 69513
姓名 サワシマ, イクコ
内容記述
内容記述タイプ Other
内容記述 There are several researches on a normed space N with the extension property : each continuous linear function f on a subspace of any normed space with values in N has a linear extension f' on the whole space such that ‖f‖=‖f'‖. Among those, the following result has been obtained by L. Nachbin [4] ; a normed space has the extension property if and only if the collection of all its spheres has the binary intersection property. The collection U of all spheres is said to have the binary intersection property if every subcollection of U, any two elements of which intersect, has a nonvoid intersection. In this paper, we shall give a convenient definition of extension property of locally convex topological vector spaces. Of course the property must be a generalization of the usual extension property. Theorem 1 gives a necessary and sufficient condition in order that a locally convex space should have the extension property in our sense which corresponds with Nachbin's result. Theorem 2 gives a characterization of a locally convex topological vector space having the extension property. A vector space E is said to be a\
topological vector space if E is a Hausdorff space in which the vector operations, summation and scalar multiplication, are continuous for the topology. Moreover, if the neighbourhood system in a topological vector space consists of convex sets, then E is said to be a locally convex topological vector space or a locally convex space. In this paper, the neighbourhood system in a locally convex space is always assumed, without loss of generality, to consist of symmetric, convex closed sets. We shall denote by R the real space (-∞, +∞) and {x ; P(x)} the set of all the elements with the property P(x).
書誌情報 お茶の水女子大學自然科學報告

巻 11, 号 1, p. 19-27, 発行日 1960-07
ISSN
収録物識別子タイプ ISSN
収録物識別子 00298190
書誌レコードID
収録物識別子タイプ NCID
収録物識別子 AN00033958
フォーマット
内容記述タイプ Other
内容記述 application/pdf
形態
611032 bytes
日本十進分類法
主題Scheme NDC
主題 400
出版者
出版者 お茶の水女子大学
資源タイプ
内容記述タイプ Other
内容記述 紀要論文
資源タイプ・ローカル
紀要論文
資源タイプ・NII
Departmental Bulletin Paper
資源タイプ・DCMI
text
資源タイプ・ローカル表示コード
03
所属
Department of Mathematics, Faculty of Science, Ochanomizu University
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