| Banach空间中Birkhoff正交性的刻画 |
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| 引用本文： | 杨冲,张登华. Banach空间中Birkhoff正交性的刻画[J]. 数学的实践与认识, 2008, 38(9): 187-192 |
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| 作者姓名： | 杨冲 张登华 |
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| 作者单位： | 1. 华北电力大学,数理系,河北,保定,071003
2. 华北电力大学,科技学院,河北,保定,071003 |
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| 摘 要： | 研究了Banach空间中两元素a和b在Birkhoff意义下正交的性质,给出在Banach空间中两个元素B-正交和线性泛函的关系,然后用线性泛函来研究B-正交性与Banach空间的可微性、凸性、自反性的关系.本文最后定义B-正交性的补,通过B-正交性的补来研究B-正交性和Banach空间的性质.
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| 关 键 词： | Birkhoff正交性 Gateaux可微性 线性泛函 自反空间 |
| 修稿时间： | 2008-01-17 |
Characterizations of Birkhoff Orthogonality in Banach Space |
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| YANG Chong,ZHANG Deng-hua. Characterizations of Birkhoff Orthogonality in Banach Space[J]. Mathematics in Practice and Theory, 2008, 38(9): 187-192 |
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| Authors: | YANG Chong ZHANG Deng-hua |
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| Abstract: | We discuss some propositions of a to be orthogonal to b in the sense of Birkhoff in a Banach space X.And we give the relations of B-orthogonality with linear functional,then use linear functional to discuss Gateaux differentiability,convexity and reflexivity in a Banach space.Last,we define B-complementary subspace,and dicuss some propositions of it. |
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| Keywords: | Birkhoff orthogonality gateaux differentiability linear functional reflexive space |
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