On some new characterizations of weakly compact sets in Banach spaces

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	On some new characterizations of weakly compact sets in Banach spaces
	Cheng, L. X. ; Cheng, Q. J. ; Luo, Z. H. ; Cheng QJ(程庆进)
刊名	http://dx.doi.org/10.4064/sm201-2-3
	2010
关键词	CONVEX-FUNCTIONS DIFFERENTIABILITY REFLEXIVITY NORMS
英文摘要	NSFC [10771175, 11071201]; We show several characterizations of weakly compact sets in Banach spaces. Given a bounded closed convex set C of a Banach space X, the following statements are equivalent: (i) C is weakly compact; (ii) C can be affinely uniformly embedded into a reflexive Banach space; (iii) there exists an equivalent norm on X which has the w2R-property on C; (iv) there is a continuous and w-lower semicontinuous seminorm p on the dual X with p >= sup(C) such that p(2) is everywhere Frechet differentiable in X; and as a consequence, the space X is a weakly compactly generated space if and only if there exists a continuous and w-l.s.c. Frechet smooth (not necessarily equivalent) norm on X*.
语种	英语
内容类型	期刊论文
源URL	[http://dspace.xmu.edu.cn/handle/2288/66508]
专题	数学科学－已发表论文
推荐引用方式 GB/T 7714	Cheng, L. X.,Cheng, Q. J.,Luo, Z. H.,et al. On some new characterizations of weakly compact sets in Banach spaces[J]. http://dx.doi.org/10.4064/sm201-2-3,2010.
APA	Cheng, L. X.,Cheng, Q. J.,Luo, Z. H.,&程庆进.(2010).On some new characterizations of weakly compact sets in Banach spaces.http://dx.doi.org/10.4064/sm201-2-3.
MLA	Cheng, L. X.,et al."On some new characterizations of weakly compact sets in Banach spaces".http://dx.doi.org/10.4064/sm201-2-3 (2010).