| dc.contributor.author | Otae, Lamech Wasonga | |
| dc.date.accessioned | 2024-11-11T11:01:31Z | |
| dc.date.available | 2024-11-11T11:01:31Z | |
| dc.date.issued | 2024 | |
| dc.identifier.uri | http://ir.jooust.ac.ke/handle/123456789/14179 | |
| dc.description.abstract | Characterizing geometric properties in Banach spaces in terms of their mappings has been done for a long period of time however it remains a very difficult task to complete due to the complex underlying structures in the Banach spaces. Recently, of interest has been the norm-attainability and orthogonality aspects in Banach space setting in general. To char- acterize these properties, one requires a geometrical view of the problem and this brings into the picture the concept of Birkhoff-James orthogo- nality in order to solve the problem. The main objective of this study is to establish norm-attainability conditions of operators via Birkhoff-James orthogonality in Banach spaces. The specific objectives include to: Es- tablish Birkhoff-James orthogonality conditions for operators in Banach spaces; Determine norm-attainability of operators in Banach spaces via Birkhoff-James orthogonality and; Investigate the relationship between the set of norm-attainable vectors and the set of norm-attainable oper- ators via Birkhoff-James orthogonality in Banach spaces. The research methodology involved the use of known orthogonality criterion in normed spaces, technical approaches such as polar decomposition and tensor prod- ucts and some known inequalities such as triangle inequality and Cauchy- Schwarz inequality. The results show that operators are norm-attainable in Banach spaces via Birkhoff-James orthogonality. Moreover, there is a strong relationship between the set of norm-attainable operators and the set of norm-attainable vectors. The results of this study are useful in understanding the concept of orthogonal projections and has applications in optimization theory and convex analysis. | en |
| dc.language.iso | en | en |
| dc.publisher | JOOUST | en |
| dc.subject | Birkhoff-James | en |
| dc.subject | Birkhoff-James Orthogonality | en |
| dc.subject | Norm-Attainability | en |
| dc.subject | Operators in Banach Spaces | en |
| dc.title | On Birkhoff-James Orthogonality and Norm-Attainability of Operators in Banach Spaces | en |
| dc.type | Thesis | en |
