Properties of best approximations with respect to the Ky Fan $p$-$k$ norm, and the strict spectral approximant of a matrix
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914490825572352 |
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| author | Grover, Priyanka Gupta, Krishna Kumar |
| author_facet | Grover, Priyanka Gupta, Krishna Kumar |
| contents | Some questions raised in [K. Ziętak, {\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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_07498 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Properties of best approximations with respect to the Ky Fan $p$-$k$ norm, and the strict spectral approximant of a matrix Grover, Priyanka Gupta, Krishna Kumar Functional Analysis 15A60, 15A18, 58C20, 47A30 Some questions raised in [K. Ziętak, {\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. |
| title | Properties of best approximations with respect to the Ky Fan $p$-$k$ norm, and the strict spectral approximant of a matrix |
| topic | Functional Analysis 15A60, 15A18, 58C20, 47A30 |
| url | https://arxiv.org/abs/2603.07498 |