The functional dimension of some classes of spaces

CSpace

	The functional dimension of some classes of spaces
	Liu, SP; Li, BR
	2005
发表期刊	CHINESE ANNALS OF MATHEMATICS SERIES B
ISSN	0252-9599
卷号	26 期号:1 页码:67-74
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.
关键词	functional dimension countable Hilbert space topological linear space
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000228149000005
出版者	SHANGHAI SCIENTIFIC TECHNOLOGY LITERATURE PUBLISHING HOUSE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/1196
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.