| 模糊赋范空间上线性算子的基本定理 |
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| 引用本文： | 肖建中,朱杏华.模糊赋范空间上线性算子的基本定理[J].中国科学技术大学学报,2004,34(4):414-430. |
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| 作者姓名： | 肖建中 朱杏华 |
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| 作者单位： | 南京信息工程大学数学系,南京,210044 |
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| 基金项目： | NNSFofEducationalDepartmentofJiangsuProvinceofChinaandScienceFoundationofNanjingUniversityofInformationScienceandTechnology |
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| 摘 要： | 研究模糊赋范空间上线性算子的基本性质 .引入算子的开性、闭性、ρ 开性、ρ 闭性等概念并讨论了它们间的关系 ;在此基础上建立了开映射定理、闭图象定理、半开映射定理、半闭图象定理、逆算子定理等 ;还给出了其中一些定理的应用 .
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| 关 键 词： | 模糊赋范空间 有界算子 ρ-有界算子 开算子 闭算子 逆算子 |
Some Basic Theorems for Linear Operators Between Fuzzy Normed Spaces |
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| Abstract.Some Basic Theorems for Linear Operators Between Fuzzy Normed Spaces[J].Journal of University of Science and Technology of China,2004,34(4):414-430. |
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| Authors: | Abstract |
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| Abstract: | Some basic properties for linear operators between fuzzy normed spaces are further studied. Firstly, the concepts of openness, closedness, ρ-openness and ρ-closedness of operators are introduced, and at the same time, the relations among them are discussed. Moreover, by making use of these concepts, a certain number of theorems are established, including the open mapping theorem, the semi-open mapping theorem, the closed graph theorem, the semi-closed graph theorem, the bounded inverse theorem and the semi-bounded inverse theorem. Finally, some applications related to these theorems are given. |
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| Keywords: | fuzzy normed linear space bounded operator ρ-bounded operator open operator closed operator inverse operator |
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