Analytical Study on Approximate 𝝐-Birkhoff-James Orthogonality

  • Saied A. Jhonny University of Baghdad
  • Buthainah A. Ahmed Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq
Keywords: Linear operator, Norm attainment, approximate 𝜖-Birkhoff-James orthogonality, reflexivity

Abstract

In this paper, we obtain a complete characterization for the norm and the minimum norm attainment sets of bounded linear operators on a real Banach spaces at a vector in the unit sphere, using approximate ðœ–-Birkhoff-James orthogonality techniques. As an application of the results, we obtained a useful characterization of
bounded linear operators on a real Banach spaces. Also, using approximate ðœ–-Birkhoff -James orthogonality proved that a Banach space is a reflexive if and only if for any closed hyperspace of , there exists a rank one linear operator such that , for some vectors in and such that 𜖠.Mathematics subject classification (2010): 46B20, 46B04, 47L05.

Published
2020-07-29
How to Cite
Jhonny, S. A., & Ahmed, B. A. (2020). Analytical Study on Approximate 𝝐-Birkhoff-James Orthogonality. Iraqi Journal of Science, 61(7), 1751-1758. https://doi.org/10.24996/ijs.2020.61.7.24
Section
Mathematics