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arXiv · 1706.07715

On approximate Birkhoff-James orthogonality and normal cones in a normed space

Debmalya Sain·Kallol Paul·Arpita mal
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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.

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Debmalya Sain, Kallol Paul, Arpita mal. 2017-06-23. On approximate Birkhoff-James orthogonality and normal cones in a normed space. https://arxiv.org/abs/1706.07715

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