Article Sidebar

Submitted
January 21, 2020
Accepted
July 15, 2020
Published
July 20, 2020
Download
PDF
Statistic
Read Counter : 354 Download : 443

Main Article Content

Abstract

In this paper we define orthogonality concept on Banach space. That is called Birkhoff-Jamesorthogonality. Some new problem about the correlation of orthogonality between Hilbert space and Birkhoff-James were discussed. Correlation investigated by using particular norm. In other side, correlation of minimum distance in Banach space and Birkhoff-James orthogonality also discussed, by generalizing minimum distance in Hilbert space 

Keywords

Banach space Birkhoff-James orthogonality minimum distance

Article Details

License

Authors who publish with this journal agree to the following terms:

  1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
  2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
  3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
How to Cite
Hariyanto, S., Udjiani, T., Sagala, Y. C., & Fadil, M. R. (2020). Finding Minimum Distance on Birkhoff-James Orthogonality in Banach Space. EKSAKTA: Journal of Sciences and Data Analysis, 20(2), 124–128. https://doi.org/10.20885/EKSAKTA.vol1.iss2.art5
Download Citation
Endnote/Zotero/Mendeley (RIS)
BibTeX
Crossref
Scopus
Google Scholar
Europe PMC

References

  1. L. Arambasic and R. Rajic, "The Birkhoff-James Orthogonality in Hilbert C*-modules," LinearAlgebra, vol. 437, pp. 1913-1929, 2012.[2] L. Arambasic and R. Rajic, "A Strong Version of the Birkhoff-James Orthogonality in Hilbert C*-modules," Annals of Functinal Analysis, vol. 1, pp. 109-120, 2014.
  2. T. Bhattacharyya and P. Grover, "Characterization of Birkhoff-James Orthogonality," Journal ofMathematical Analysis and Applications, vol. 407, pp. 350-358, 2013.
  3. P. Grover, "Orthogonality to Matrix Subspaces, and a Distance Formula," Linear Algebra, vol. 445,pp. 280-288, 2014.
  4. D. Sain, K. Paul and S. Hait, "Operator Norm Attainment and Birkhoff-James Orthogonality," LinearAlgebra, vol. 476, pp. 85-97, 2015.
  5. K. Paul, D. Sain and P. Ghosh, "Birkhoff-James Orthogonality and Smoothness of Bounded LinearOperators," Linear Algebra, vol. 506, pp. 551-563, 2016.
  6. P. Ghosh, D. Sain and K. Paul, "On Symmetry of Birkhoff-James Orthogonality of Linear Operators,"Advance in Operator Theory, vol. 4, pp. 428-434, 2017.
  7. E. Kreyszig, Introductory Functional Analysis with Applications, New York: John Wiley & Sons,Inc, 1978.
  8. A. Dax, "The Distance between Two Convex Sets," Linear Algebra and its Applications, pp. 184-213,2006.
  9. A. Iske, Approximation Theory and Algorithms for Data Analysis, Switzerland: Springer Nature Switzerland, 2010.
  10. D. G. Luenberger, Optimization by Vector Space Methods, New York: John Wiley & Sons, Inc, 1969.
  11. F. Deutsch, Best Approximation in Inner product Spaces, New York: Springer Verlag, Inc, 2001.
  12. J. Weidmann, Linear Operator in Hilbert Spaces, New York: Springer-Verlag New York, 1980.