Properties of Fuzzy Compact Linear Operators on Fuzzy Normed Spaces

• Main Author: Kider et al.
• Format: Article
• Language: Arabic
• Published: College of Science for Women, University of Baghdad 2019-03-01
• Series: Baghdad Science Journal
• Subjects: Complete fuzzy normed space, Fuzzy normed space, Fuzzy bounded operator, Fuzzy compact operator, Relatively compact set.
• Online Access: http://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/3188

In this paper the definition of fuzzy normed space is recalled and its basic properties. Then the definition of fuzzy compact operator from fuzzy normed space into another fuzzy normed space is introduced after that the proof of an operator is fuzzy compact if and only if the image of any fuzzy bounded sequence contains a convergent subsequence is given. At this point the basic properties of the vector space FC(V,U)of all fuzzy compact linear operators are investigated such as when U is complete and the sequence ( ) of fuzzy compact operators converges to an operator T then T must be fuzzy compact. Furthermore we see that when T is a fuzzy compact operator and S is a fuzzy bounded operator then the composition TS and ST are fuzzy compact operators. Finally, if T belongs to FC(V,U) and dimension of V is finite then T is fuzzy compact is proved.