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Locally Convex Spaces with the Extension Property
http://hdl.handle.net/10083/2082
http://hdl.handle.net/10083/2082904a05a2-98d3-4f01-8f95-67b76161a2af
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
KJ00004829511.pdf (611.0 kB)
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| Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
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| 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× 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). |
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| 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 |
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| 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 | ||||||
