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
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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). |
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