| 关于拟线性算子的几个性质 |
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| 引用本文： | 盖功琪.关于拟线性算子的几个性质[J].黑龙江大学自然科学学报,2007,24(2):261-262. |
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| 作者姓名： | 盖功琪 |
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| 作者单位： | 哈尔滨学院,数学与计算机学院,黑龙江,哈尔滨,150080 |
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| 基金项目： | 黑龙江省教育厅科学技术研究项目 |
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| 摘 要： | 首先给出拟线性算子定义,讨论了算子的齐性、拟可加性和幂等的一些关系,证明了在一定条件下算子的拟线性和拟可加性的等价性,并证明了拟线性算子值域的闭性,得到拟线性算子值域中的连续性,给出了有界拟线性算子的广义Banach引理.
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| 关 键 词： | 拟线性算子 齐性 Banach空间 |
| 文章编号： | 1001-7011(2007)02-0261-02 |
| 修稿时间： | 2006年1月12日 |
On some properties of quasi -linear operator |
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| GAI Gong-qi.On some properties of quasi -linear operator[J].Journal of Natural Science of Heilongjiang University,2007,24(2):261-262. |
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| Authors: | GAI Gong-qi |
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| Abstract: | The definition of quasi-linearity operators is first given,and then the relations of homogeneity,the quasi-additivity and idempotence of operators are discussed.In certain condition it has proven equivalence between the quasi-linearity and quasi-additivity of operators,and has proven that the range of the quasi-linear operators is closed.Continuity of the quasi-linear operators is obtained in its range,and a generalized Banach lemma for the bounded Quasi-linear operator in Banach space is given. |
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| Keywords: | quasi-linear operator homogeneity Banach space |
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