• Login
  • Help Guide
View Item 
  •   JOOUST IR Home
  • Theses & Dissertations
  • Doctor of Philosophy Theses and Dissertations
  • School of Biological, Physical, Mathematics & Actuarial Sciences
  • View Item
  •   JOOUST IR Home
  • Theses & Dissertations
  • Doctor of Philosophy Theses and Dissertations
  • School of Biological, Physical, Mathematics & Actuarial Sciences
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

On Birkhoff-James Orthogonality and Norm-Attainability of Operators in Banach Spaces

Thumbnail
View/Open
Otae_On Birkhoff-James Orthogonality and Norm-Attainability of.pdf (270.6Kb)
Publication Date
2024
Author
Otae, Lamech Wasonga
Type
Thesis
Metadata
Show full item record
Abstract/Overview

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.

Subject/Keywords
Birkhoff-James; Birkhoff-James Orthogonality; Norm-Attainability; Operators in Banach Spaces
Publisher
JOOUST
Permalink
http://ir.jooust.ac.ke/handle/123456789/14179
Collections
  • School of Biological, Physical, Mathematics & Actuarial Sciences [55]

Browse

All of JOOUST IRCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

My Account

LoginRegister

Statistics

View Usage Statistics

Contact Us

Copyright © 2023-4 Jaramogi Oginga Odinga University of Science and Technology (JOOUST)
P.O. Box 210 - 40601
Bondo – Kenya

Useful Links

  • Report a problem with the content
  • Accessibility Policy
  • Deaccession/Takedown Policy

TwitterFacebookYouTubeInstagram

  • University Policies
  • Access to Information
  • JOOUST Quality Statement