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 .
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.
基金
NNSFofEducationalDepartmentofJiangsuProvinceofChinaandScienceFoundationofNanjingUniversityofInformationScienceandTechnology
关键词
模糊赋范空间
有界算子
p-有界算子
开算子
闭算子
逆算子
fuzzy normed linear space
bounded operator
ρ-bounded operator
open operator
closed operator
inverse operator
