Birkhoff Orthogonality and Different Particular Cases of Carlsson's Orthogonality on Normed Linear Spaces
- 1 Kirtipur, Nepal
Abstract
Let x, y ∈ X, where X is an inner-product space. We say x is orthogonal to y if ⟨x, y⟩ = 0. When we move to general normed spaces there are many possibilities of extending the notion of orthogonality. Since 1934, different types of orthogonality relations in normed spaces have been introduced and studied. In this study, we enlist some properties of Birkhoff's orthogonality and Carlsson's orthogonality along with it we introduce two new particular cases of Carlsson's orthogonality and check some properties of othogonality in relation to these particular cases in normed spaces.
DOI: https://doi.org/10.3844/jmssp.2020.133.141
Copyright: © 2020 Prakash Muni Bajracharya and Bhuwan Prasad Ojha. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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Keywords
- Birkhoff Orthogonality
- Carlsson Orthogonality
- Minkowski Plane
- Pythagorean Orthogonality
- Robert Orthogonality