English

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}
}