| 赋Luxemburg范数的Orlicz-Bochner空间的端点与严格凸性 |
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| 引用本文： | 刘玉霞,石忠锐,张品. 赋Luxemburg范数的Orlicz-Bochner空间的端点与严格凸性[J]. 上海大学学报(英文版), 2003, 7(4): 322-326. DOI: 10.1007/s11741-003-0004-0 |
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| 作者姓名： | 刘玉霞 石忠锐 张品 |
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| 作者单位： | Department of Mathematics，College of Sciences，Shanghai University，Shanghai 200072，China，Department of Mathematics，College of Sciences，Shanghai University，Shanghai 200072，China，Department of Mathematics，College of Sciences，Shanghai University，Shanghai 200072，China |
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| 基金项目： | theNationalNaturalScienceFoun dationofChina (GrantNo .199710 2 2 ) |
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| 摘 要： | LetB(X)andS(X)standfortheunitballandunitsphereofanormedspaceX ,respectively .x∈S(X)iscalledanextremepointofB(X) providedthatfory ,z∈B(X) ,x =y z2 implies y =z .DenotethesetofallextremepointsofB(X)byExtB(X) .XiscalledrotundprovidedthatS(X) =ExtB(X) .Therotundspacesarerelatedtotheoperationresearch ,thecontroltheory ,etc[1] . LetΦbeaevenconvexfunctionwithΦ(0 ) =0 ;Φ(u) >0 (u≠ 0 ) ;limu→ ∞ Φ (u) = ∞ .LetXbeanormedspace ,G Rnbeaboundedmeasurableset ,and (G ,∑ ,μ)beameasur…
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| 关 键 词： | Orlicz-Bochner空间 Luxemburg范数 生成函数 极值点 |
| 收稿时间： | 2002-12-04 |
Rotundity of Orlicz-Bochner space with Luxemburg norm |
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| Liu Yu-Xia,Shi Zhong-Rui,Zhang Pin. Rotundity of Orlicz-Bochner space with Luxemburg norm[J]. Journal of Shanghai University(English Edition), 2003, 7(4): 322-326. DOI: 10.1007/s11741-003-0004-0 |
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| Authors: | Liu Yu-Xia Shi Zhong-Rui Zhang Pin |
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| Affiliation: | Department o f Mathematics, College o f Sciences, Shanghai University, Shanghai 200072, China |
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| Abstract: | In this paper, by using the generating function Φ and X the criteria of the rotundity for the Orlicz-Bochner function and sequence spaces endowed with the Luxemburg norm were obtained. And the sufficient and necessary conditions were given for the extreme point of Orlicz-Bochner sequence space and the conditions in part for Orlicz-Bochner function space. Project supported in part by the National Natural Science Foundation of China (Grant No. 19971022) |
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| Keywords: | extreme point rotundity Orlicz-Bochner space Luxemgury norm. |
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