Properties of Fuzzy Compact Linear Operators on Fuzzy Normed Spaces
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 bou...
Main Author: | |
---|---|
Format: | Article |
Language: | Arabic |
Published: |
College of Science for Women, University of Baghdad
2019-03-01
|
Series: | Baghdad Science Journal |
Subjects: | |
Online Access: | http://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/3188 |
id |
doaj-65e91ce863554f92a0ab1df3f5e2f402 |
---|---|
record_format |
Article |
spelling |
doaj-65e91ce863554f92a0ab1df3f5e2f4022020-11-25T01:49:59ZaraCollege of Science for Women, University of BaghdadBaghdad Science Journal2078-86652411-79862019-03-0116110.21123/bsj.16.1.01043188Properties of Fuzzy Compact Linear Operators on Fuzzy Normed SpacesKider et al. 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. http://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/3188Complete fuzzy normed space, Fuzzy normed space, Fuzzy bounded operator, Fuzzy compact operator, Relatively compact set. |
collection |
DOAJ |
language |
Arabic |
format |
Article |
sources |
DOAJ |
author |
Kider et al. |
spellingShingle |
Kider et al. Properties of Fuzzy Compact Linear Operators on Fuzzy Normed Spaces Baghdad Science Journal Complete fuzzy normed space, Fuzzy normed space, Fuzzy bounded operator, Fuzzy compact operator, Relatively compact set. |
author_facet |
Kider et al. |
author_sort |
Kider et al. |
title |
Properties of Fuzzy Compact Linear Operators on Fuzzy Normed Spaces |
title_short |
Properties of Fuzzy Compact Linear Operators on Fuzzy Normed Spaces |
title_full |
Properties of Fuzzy Compact Linear Operators on Fuzzy Normed Spaces |
title_fullStr |
Properties of Fuzzy Compact Linear Operators on Fuzzy Normed Spaces |
title_full_unstemmed |
Properties of Fuzzy Compact Linear Operators on Fuzzy Normed Spaces |
title_sort |
properties of fuzzy compact linear operators on fuzzy normed spaces |
publisher |
College of Science for Women, University of Baghdad |
series |
Baghdad Science Journal |
issn |
2078-8665 2411-7986 |
publishDate |
2019-03-01 |
description |
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.
|
topic |
Complete fuzzy normed space, Fuzzy normed space, Fuzzy bounded operator, Fuzzy compact operator, Relatively compact set. |
url |
http://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/3188 |
work_keys_str_mv |
AT kideretal propertiesoffuzzycompactlinearoperatorsonfuzzynormedspaces |
_version_ |
1725003570594447360 |