| 李新宝.实赋范数性空间内的Lp-正交[J].数学研究及应用,1991,11(4):517~521 |
| 实赋范数性空间内的Lp-正交 |
| Lp- Orthogonality in Real Normed Linear Spaces |
| 投稿时间：1988-05-03 |
| DOI：10.3770/j.issn:1000-341X.1991.04.008 |
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| In this paper we have proved the theorem: Let p>1, and E be a real normed linear space, if the Lp-orthogonality in E satisfies one of the following conditions 1) homogeneity 2) additivity 3) x⊥Lpy implies x⊥Jy 4) x⊥Jy implies x⊥Lpy, then E is an abstract Euclidean space and there must be p=2. We also proved anR. C. James' result-If for every element x of a normed linear space E therecan be found a nonzero element orthogonal to x by Roberts' definition in each two dimensional linear subset containing x, then E is an abstract Euclidean space——which had not been proved. Finally, we point out that if one of the James′,Lp-,isosceles, Pythagorean and (α,β)-orthogonalities defined in E implies Roberts′ orthogonality then E is an abstract Euclidean space. |
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