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arXiv · 2603.07498

Properties of best approximations with respect to the Ky Fan $p$-$k$ norm, and the strict spectral approximant of a matrix

Priyanka Grover·Krishna Kumar Gupta
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Abstract

Some questions raised in [K. Zi\k{e}tak, {\it From the strict Chebyshev approximant of a vector to the strict spectral approximant of a matrix}, Warsaw : Banach Center Publ., 112 Polish Acad. Sci. Inst. Math. (2017)] are discussed. To do so, the subdifferential set of the Ky Fan $p$-$k$ norm is computed. A characterization for the best approximations with respect to the Ky Fan $p$-$k$ norms is given. Further, necessary and sufficient conditions for $\varepsilon$-Birkhoff orthogonality with respect to the Ky Fan $p$-$k$ norm are also derived.

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Priyanka Grover, Krishna Kumar Gupta. 2026-03-08. Properties of best approximations with respect to the Ky Fan $p$-$k$ norm, and the strict spectral approximant of a matrix. https://arxiv.org/abs/2603.07498

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