On approximate Birkhoff-James orthogonality and normal cones in a normed space
Functional Analysis
2024-07-30 v1
Abstract
We study two notions of approximate Birkhoff-James orthogonality in a normed space, from a geometric point of view, and characterize them in terms of normal cones. We further explore the interconnection between normal cones and approximate Birkhoff-James orthogonality to obtain a complete characterization of normal cones in a two-dimensional smooth Banach space. We also obtain a uniqueness theorem for approximate Birkhoff-James orthogonality set in a normed space.
Keywords
Cite
@article{arxiv.1706.07715,
title = {On approximate Birkhoff-James orthogonality and normal cones in a normed space},
author = {Debmalya Sain and Kallol Paul and Arpita mal},
journal= {arXiv preprint arXiv:1706.07715},
year = {2024}
}