| Banach空间中线性算子的(集值)度量广义逆的表示及应用 |
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| 引用本文： | 倪仁兴. Banach空间中线性算子的(集值)度量广义逆的表示及应用[J]. 系统科学与数学, 2006, 26(6): 714-719 |
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| 作者姓名： | 倪仁兴 |
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| 作者单位： | 绍兴文理学院数学系,绍兴,312000 |
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| 基金项目： | 国家自然科学基金资助项目(10271025)浙江省自然科学基金资助项目(102002)． |
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| 摘 要： | 在Banach空间Y无自反和从Banach空间X到Y的线性算子T无闭值域和稠定的假定下,利用Banach空间几何方法证明了Banach空间中线性算子的度量广义逆是具有闭凸值的集值映射,建立了该度量广义逆的存在性、唯一性和等价表达式,并给出了此表达式的一个应用示例．所得的部分结果本质地拓广王玉文和潘少荣在Banach空间Y自反,从X到Y的线性算子T为闭值域和稠定的假定下的近期相应结果．
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| 关 键 词： | 线性算子 度量广义逆 正规对偶映射 集值映射 凸二次规划 |
| 收稿时间： | 2004-03-03 |
| 修稿时间： | 2004-03-03 |
The representation of the set-valued metric generalized inverse of linear operator in Banach space and its application |
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| Ni Renxing. The representation of the set-valued metric generalized inverse of linear operator in Banach space and its application[J]. Journal of Systems Science and Mathematical Sciences, 2006, 26(6): 714-719 |
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| Authors: | Ni Renxing |
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| Affiliation: | Department of Mathematics, Shaoxing University, Shaoxing 312000 |
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| Abstract: | Without the assumption that Banach space Y is reflexive and T is a densely defined linear operator with closed range from Banach space X to Y, it is proved that the metric generalized inverse of linear operator has closed convex range set-valued mapping by means of geometry of Banach space. Existence, uniqueness and the equivalent representation of the metric generalized inverse are established, and an application example of the representation is given. Parts of our results have extended and improved the corresponding recent results obtained by Wang Yu-wen and Pan Shao-rong under the above-mentioned assumption. |
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| Keywords: | Linear operator metric generalized inverse normalized duality mapping set-valued mapping convex quadratic programming. |
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