| 赋Luxemburg范数的Orlicz-Bochner空间的收敛性的一个注记 |
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| 引用本文： | 张剑尘.赋Luxemburg范数的Orlicz-Bochner空间的收敛性的一个注记[J].上海大学学报(英文版),2003,7(4):358-360. |
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| 作者姓名： | 张剑尘 |
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| 作者单位： | Department of |
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| 基金项目： | theNationalNaturalScienceFoundationofChina (GrantNo.199710 2 2 ) |
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| 摘 要： | LetΦbeaconvexevenfunctionwithΦ(0 ) =0 ;Φ(u) >0 (u≠ 0 ) ;limu→ ∞ Φ(u) = ∞ ,Xbeanormedspace ,I=0 ,1].ForafunctionxfromIintoXwithx(t) =limn ∑m(n)i=1ai|Ei,ai∈X ,themodularisdefinedasρΦ(x) =∫IΦ(‖x(t)‖ )dt.TheOrlicz BochnersetisLΦ(I,X) ={x(t) : λ >0 ,ρΦ(λx) <∞ }thenLΦ(I ,X)isalinearset.Let‖x‖ =inf{λ >0 :ρΦ(xλ)≤ 1}whilexisendowedwithsuchanormandXisaBa nachspace ,LΦ(I,X)formsaBanachspace .Forxandxn∈X ,xiscalledaconvergentpointofxnif‖x -xn‖→ 0 .Φissaidtosa…
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| 关 键 词： | 收敛性 Orlicz-Bochner空间 Luxemburg范数 Banach空间 |
| 收稿时间： | 17 January 2003 |
A note on the convergence of Orlicz-Bochner spaces with the Luxemburg norm |
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| Zhang?Jian-Chen.A note on the convergence of Orlicz-Bochner spaces with the Luxemburg norm[J].Journal of Shanghai University(English Edition),2003,7(4):358-360. |
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| Authors: | Zhang Jian-Chen |
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| Institution: | Department of Mathematics, College of Sciences, Shanghai University, Shanghai 200436, China |
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| Abstract: | In this paper, the convergence of the Orlicz-Bochner function spaces with the Luxemburg norm was proved. |
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| Keywords: | convergence modular Orlicz-Bochner space Luxemgurg norm |
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