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arXiv · 2407.20102

On the best coapproximation problem in $\ell_1^n$

Debmalya Sain·Shamim Sohel·Souvik Ghosh·Kallol Paul
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Abstract

We study the best coapproximation problem in the Banach space $ \ell_1^n, $ by using Birkhoff-James orthogonality techniques. Given a subspace $\mathbb{{Y}}$ of $\ell_1^n$, we completely identify the elements $x$ in $\ell_1^n,$ for which best coapproximations to $x$ out of $\mathbb{{Y}}$ exist. The methods developed in this article are computationally effective and it allows us to present an algorithmic approach to the concerned problem. We also identify the coproximinal subspaces and co-Chebyshev subspaces of $\ell_1^n$.

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Debmalya Sain, Shamim Sohel, Souvik Ghosh, Kallol Paul. 2024-07-29. On the best coapproximation problem in $\ell_1^n$. https://doi.org/10.1080/03081087.2022.2153101

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