[1]罗正华.弱紧集上的2-Rotund范数[J].华侨大学学报(自然科学版),2012,33(3):357-360.[doi:10.11830/ISSN.1000-5013.2012.03.0357]
　LUO Zheng-hua.2-Rotund Norms on the Weakly Comapct Sets[J].Journal of Huaqiao University(Natural Science),2012,33(3):357-360.[doi:10.11830/ISSN.1000-5013.2012.03.0357]
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弱紧集上的2-Rotund范数()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第33卷
期数:
2012年第3期
页码:
357-360
栏目:
出版日期:
2012-05-20

文章信息/Info

Title:
2-Rotund Norms on the Weakly Comapct Sets
文章编号:
1000-5013(2012)03-0357-04
作者:
罗正华
华侨大学数学科学学院
Author(s):
LUO Zheng-hua
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
关键词:
Banach空间;  弱紧集;  2R范数;  w2R范数
Keywords:
Banach spaces;  weakly compact sets;  2R norms;  w2R norms
分类号:
O177.2
DOI:
10.11830/ISSN.1000-5013.2012.03.0357
文献标志码:
A
摘要:
设C是Banach空间(X,‖.‖)弱紧凸子集,P为X上等价范数的全体,证明X在C上满足weakly 2-Rotund(w2R)性质的等价范数全体为P的剩余集; 当C是可分时,上述w2R性质可替换为2R性质,推广了罗正华的研究结论.
Abstract:
Let C be a weakly compact convex subset of a Banach space(X,‖·‖) and P be the set of all the equivalent norms on X,we prove that all the equivalent norms on X which satisfy the weakly 2-Rotund(w2R) property on C form a residual set of P.In Addition,if C is separable,the above w2R property can be replaced by 2R property.This result generalize the one made by LUO Zheng-hua.

参考文献/References:

[1] MILMAN D P. On some criteria for the regularity of spaces of the type (B) [J]. Doklady Akademii Nauk SSSR, 1938.243-246.
[2] PETTIS B J. A proof that every uniformly convex spaces is reflexive [J]. Duke Mathematical Journal, 1939(2):249-253.
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[5] DAY M M. Normed linear spaces [D]. New York:springer-verlag, 1973.
[6] TROYANSKI S. On locally uniformly convex and differentiable norms in certain nonseparable Banach spaces [J]. Studia Mathematica, 1972.125-138.
[7] DEVILLE R, GODEFROY G, ZIZLER V. Smoothness and renormings in Banach spaces [M]. New York:John Wiley and Sons, Inc, 1993.
[8] HAJEK P, JOHANIS M. Characterization of reflexivity by equivalent renorming [J]. Journal of Functional Analysis, 2004(1):163-172.doi:10.1016/S0022-1236(03)00264-7.
[9] ODELL E, SCHLUMPRECHT T. Asymptotic properties of Banach spaces under renormings [J]. Journal of the American Mathematical Society, 1998(1):175-188.doi:10.1090/S0894-0347-98-00251-3.
[10] 罗正华. 关于2R(w2R)范数的一个注记 [J]. 数学研究, 2010(4):387-392.doi:10.3969/j.issn.1006-6837.2010.04.011.
[11] CHENG Li-xin, CHENG Qing-jin, LUO Zheng-hua. On some new characterizations of weakly comapct sets in Banach spaces [J]. Studia Mathematica, 2010.155-166.doi:10.4064/sm201-2-3.
[12] CHENG Li-xin, CHENG Qing-jin, LUO Zheng-hua. Every weakly compact convex set can be uniformly embedded into a reflexive space [J]. Acta Math Sin (Engl Ser), 2009(7):1109-1112.doi:10.1007/s10114-009-7545-5.

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备注/Memo

备注/Memo:
华侨大学高层次人才科研启动项目(11BS223)
更新日期/Last Update: 2014-03-23