A Study on Fuzzy Order Bounded Linear Operators in Fuzzy Riesz Spaces
This paper aims to study fuzzy order bounded linear operators between two fuzzy Riesz spaces. Two lattice operations are defined to make the set of all bounded linear operators as a fuzzy Riesz space when the codomain is fuzzy Dedekind complete. As a special case, separation property in fuzzy order...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/13/1512 |
| _version_ | 1797528543990644736 |
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| author | Juan Luis García Guirao Mobashir Iqbal Zia Bashir Tabasam Rashid |
| author_facet | Juan Luis García Guirao Mobashir Iqbal Zia Bashir Tabasam Rashid |
| author_sort | Juan Luis García Guirao |
| collection | DOAJ |
| description | This paper aims to study fuzzy order bounded linear operators between two fuzzy Riesz spaces. Two lattice operations are defined to make the set of all bounded linear operators as a fuzzy Riesz space when the codomain is fuzzy Dedekind complete. As a special case, separation property in fuzzy order dual is studied. Furthermore, we studied fuzzy norms compatible with fuzzy ordering (fuzzy norm Riesz space) and discussed the relation between the fuzzy order dual and topological dual of a locally convex solid fuzzy Riesz space. |
| first_indexed | 2024-03-10T09:59:52Z |
| format | Article |
| id | doaj.art-a274a07ac9274321b864bcb108e02062 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T09:59:52Z |
| publishDate | 2021-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-a274a07ac9274321b864bcb108e020622023-11-22T02:02:20ZengMDPI AGMathematics2227-73902021-06-01913151210.3390/math9131512A Study on Fuzzy Order Bounded Linear Operators in Fuzzy Riesz SpacesJuan Luis García Guirao0Mobashir Iqbal1Zia Bashir2Tabasam Rashid3Departamento de Matemática Aplicada y Estadástica, Universidad Politácnica de Cartagena, Hospital de Marina, 30203 Murcia, SpainDepartment of Mathematics, Quaid-i-Azam University, Islamabad 45320, PakistanDepartment of Mathematics, Quaid-i-Azam University, Islamabad 45320, PakistanDepartment of Mathematics, University of Management and Technology, Lahore 54770, PakistanThis paper aims to study fuzzy order bounded linear operators between two fuzzy Riesz spaces. Two lattice operations are defined to make the set of all bounded linear operators as a fuzzy Riesz space when the codomain is fuzzy Dedekind complete. As a special case, separation property in fuzzy order dual is studied. Furthermore, we studied fuzzy norms compatible with fuzzy ordering (fuzzy norm Riesz space) and discussed the relation between the fuzzy order dual and topological dual of a locally convex solid fuzzy Riesz space.https://www.mdpi.com/2227-7390/9/13/1512fuzzy order bounded operatorsfuzzy order dual spacesfuzzy norm riesz spaceslocally convex-solid fuzzy riesz spaces |
| spellingShingle | Juan Luis García Guirao Mobashir Iqbal Zia Bashir Tabasam Rashid A Study on Fuzzy Order Bounded Linear Operators in Fuzzy Riesz Spaces Mathematics fuzzy order bounded operators fuzzy order dual spaces fuzzy norm riesz spaces locally convex-solid fuzzy riesz spaces |
| title | A Study on Fuzzy Order Bounded Linear Operators in Fuzzy Riesz Spaces |
| title_full | A Study on Fuzzy Order Bounded Linear Operators in Fuzzy Riesz Spaces |
| title_fullStr | A Study on Fuzzy Order Bounded Linear Operators in Fuzzy Riesz Spaces |
| title_full_unstemmed | A Study on Fuzzy Order Bounded Linear Operators in Fuzzy Riesz Spaces |
| title_short | A Study on Fuzzy Order Bounded Linear Operators in Fuzzy Riesz Spaces |
| title_sort | study on fuzzy order bounded linear operators in fuzzy riesz spaces |
| topic | fuzzy order bounded operators fuzzy order dual spaces fuzzy norm riesz spaces locally convex-solid fuzzy riesz spaces |
| url | https://www.mdpi.com/2227-7390/9/13/1512 |
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