模糊赋范空间中的有界性与算子的紧性  

Boundedness and compactness of operators in fuzzy normed spaces

作　　者：李欣欣 吴健荣[1] LI Xinxin;WU Jianrong(School of Mathematics and Physics,SUST,Suzhou 215009,China)

机构地区：[1]苏州科技大学数理学院,江苏苏州215009

出　　处：《苏州科技大学学报（自然科学版）》2020年第2期18-25,共8页Journal of Suzhou University of Science and Technology（Natural Science Edition）

基　　金：国家自然科学基金资助项目(11971343)。

摘　　要：集合的有界性与算子的紧性密切相关,两者在泛函分析理论中有重要作用。利用上下确界的方法,在模糊赋范空间中提出了模糊有界、模糊强有界和模糊弱有界的定义,并得到了三者的刻画,深化了模糊赋范空间中有界性的研究。在此基础上,引入了S-模糊紧算子的概念,得到了S-模糊紧算子的一些相关性质,进一步丰富了模糊泛函空间的算子理论。The boundedness of subsets and the compactness of operators are closely related,and they play important roles in functional analysis theory.Using the supremum and infimum,we proposed the definitions of fuzzy boundedness,strongly fuzzy boundedness,and weakly fuzzy boundedness for subsets in a fuzzy normed space,and obtained their characterizations.This deepens the conclusions about the boundedness of fuzzy normed spaces.On these bases,the concept of S-fuzzy compact operator was introduced,and some properties of S-fuzzy compact operator were given,which further enriches the operator theory of fuzzy functional spaces.

关 键 词：模糊分析 模糊赋范空间 有界性 S-模糊紧算子 

分 类 号：O177.3[理学—数学]