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2-HH Norm and Birkhoff-James Orthogonality in Normed Spaces

Bhuwan Prasad Ojha*, Prakash Muni Bajracharya**

*-** Department of Mathematics at Tribhuvan University, Kathmandu, Nepal.

Periodicity:July - September'2019
DOI : https://doi.org/10.26634/jmat.8.3.16746

Abstract

For any normed space X, the p-HH norms X were introduced by Kikianty and Dragomir on X² = X x X of normed spaces. p- norms and p-HH norms induce the same topology, so they are equivalent, but are geometrically different. Besides that, E. Kikianty and S. S. Dragimor introduced HH-P orthogonality and HH-I orthogonality by using 2-HH norm and discussed main properties of these orthogonalities. The main purpose of this paper is to focus on the concept of 2-HH norm to Birkhoff and a new orthogonality in normed spaces, and we discuss some properties of these orthogonalities. It is proved that Robert orthogonality via 2-HH norm implies Birkhoff-James orthogonality via 2-HH norm; however, it is not necessary for the converse part.

Keywords

Birkhoff Orthogonality, Robert Orthogonality, p-HH Norm.

How to Cite this Article?

Ojha, B. P., and Bajracharya, P. M. (2019). 2-HH Norm and Birkhoff-James Orthogonality in Normed Spaces. i-manager's Journal on Mathematics, 8(3), 1-9. https://doi.org/10.26634/jmat.8.3.16746

References

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