| 关于Orlicz-Bochner序列空间的一些注记 |
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| 引用本文： | 张品,石忠锐,刘玉霞.关于Orlicz-Bochner序列空间的一些注记[J].上海大学学报(英文版),2005,9(1):25-28. |
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| 作者姓名： | 张品 石忠锐 刘玉霞 |
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| 作者单位： | [1]ShanghaiInstituteofAppliedMathematicsandMechanics,ShanghaiUniversity,Shanghai200072,P.R.China [2]DepartmentofMathematics,CollegeofSciences,ShanghaiUniversity,Shanghai200444,P.R.China |
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| 摘 要： | In this paper, we discuss some basic properties of the Orlicz-Bochner sequence space lM (X) and its subspace hM (X). We present the equivalent definition of hM (X), the sufficient and necessary conditions under which l(M) (X) is complete, and lM (X) and hM (X) are separable respectively, and also give the sufficient condition that hM (X) has a basis. All these results generalize the results for the classical Orlicz sequence spaces.
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| 关 键 词： | Orlicz-Bochner序列空间 完全值 可分离性 赋范线性空间 |
| 收稿时间： | 21 July 2003 |
Some notes on orlicz-bochner sequence spaces |
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| Zhang?Pin,Shi?Zhong-rui,Liu?Yu-Xia.Some notes on orlicz-bochner sequence spaces[J].Journal of Shanghai University(English Edition),2005,9(1):25-28. |
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| Authors: | Zhang Pin Shi Zhong-rui Liu Yu-Xia |
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| Institution: | 1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P.R. China
2. Department of Mathematics, College of Sciences, Shanghai University, Shanghai 200444, P.R. China |
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| Abstract: | In this paper, we discuss some basic properties of the Orlicz-Bochner sequence space l_M(X) and its subspace h_M(X). We present the equivalent definition of h_M(X), the sufficient and necessary conditions under which l_~(M) (X) is complete, and l_M(X) and h_M(X) are separable respectively, and also give the sufficient condition that h_M(X) has a basis. All these results generalize the results for the classical Orlicz sequence spaces. |
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| Keywords: | Orlicz-Bochner sequence spaces completeness separability basis |
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