Orlicz序列空间的粗系数

Abstract

Abstract:

It is proved that the roughness coefficient of Orlicz squence space

R(l_m)=2/sup_‖y‖⁰_N k_y^* ,where k^*_y=min{k>0:‖y‖⁰_N=1(1+ρ_N(ky))/k}.

Key words: Ｏｒｌｉｃｚｓｅｑｕｅｎｃｅｓｐａｃｅ, Ｒｏｕｇｈｎｅｓｓ, Ｒｏｕｇｈｎｅｓｓｃｏｅｆｆｉｃｉｅｎｔ

CLC Number:

４６Ｂ，４６Ｅ

Cite this article

Wang Quandi Wang Tingfu. The Roughness Coefficient of Orlicz Sequence Spaces[J].Acta mathematica scientia,Series A, 1999, 19(1): 80-84.

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References

1 Leach F B, Whitefield H M. Differentiable functions and rough norms on Banach spaces. Proc Amer Math Soc, 1973, 33:120-136

2 Godini G. Rough and strong rough norms on Banach spaces. Ibid, 1980, 87:239-246

3 John K, Zizler Y. On rough norms on Banach spaces, Comment. Math Univ Carolinae, 1987,19:335-349

4 李小健. Banach空间的粗范数和不可微性.数学年刊，1983，8A：621-625

5 Cui Yunan, Wang Tingfu. The roughnesses of the norms on Orlicz spaces. Comment Math(Prace Mat), 1991,31:49-57

6 Wang Tingfu, Cui Yunan, Wang Quandi. The roughness coefficient of Orlicz spaces. Ibid, 1994,34:237-245

7 崔云安，王廷辅. Orlicz序列空间的粗性. 哈尔滨科技大学学报，1993，17(4):70-75

8 Krasnoselskiǐ M A, Rutickiǐ Ya B. Convex functions and Orlicz spaces. Groningen, 1961

9 Chen Shutao. Geometry of Orlicz spaces. Dissertationes Mathematicae 356, Warszawa 1996

10 王廷辅，王全迪. 关于Orlicz空间k_x的几点注记. 工程数学学报，1994，11(2)：7-14

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The Roughness Coefficient of Orlicz Sequence Spaces

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