The functional dimension of some classes of spaces
文献类型：期刊论文
| 作者 | Liu, SP; Li, BR |
| 刊名 | CHINESE ANNALS OF MATHEMATICS SERIES B
 |
| 出版日期 | 2005 |
| 卷号 | 26期号:1页码:67-74 |
| 关键词 | functional dimension countable Hilbert space topological linear space |
| ISSN号 | 0252-9599 |
| 英文摘要 | The functional dimension of countable Hilbert spaces has been discussed by some authors. They showed that every countable Hilbert space with finite functional dimension is nuclear. In this paper the authors do further research on the functional dimension, and obtain the following results: (1) They construct a countable Hilbert space, which is nuclear, but its functional dimension is infinite. (2) The functional dimension of a Banach space is finite if and only if this space is finite dimensional. (3) Let B be a Banach space, B* be its dual, and denote the weak * topology of B* by a(B*, B). Then the functional dimension of (B*, sigma(B*, B)) is 1. By the third result, a class of topological linear spaces with finite functional dimension is presented. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000228149000005 |
| 出版者 | SHANGHAI SCIENTIFIC TECHNOLOGY LITERATURE PUBLISHING HOUSE |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/1195]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Liu, SP |
| 作者单位 | Chinese Acad Sci, Inst Math, Acad Math & Syst Sci, Beijing 100080, Peoples R China |
| 推荐引用方式 GB/T 7714 | Liu, SP,Li, BR. The functional dimension of some classes of spaces[J]. CHINESE ANNALS OF MATHEMATICS SERIES B,2005,26(1):67-74. |
| APA | Liu, SP,&Li, BR.(2005).The functional dimension of some classes of spaces.CHINESE ANNALS OF MATHEMATICS SERIES B,26(1),67-74. |
| MLA | Liu, SP,et al."The functional dimension of some classes of spaces".CHINESE ANNALS OF MATHEMATICS SERIES B 26.1(2005):67-74. |
入库方式： OAI收割
来源：数学与系统科学研究院
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