Properties of best approximations with respect to the Ky Fan p-k norm, and the strict spectral approximant of a matrix
Abstract
Some questions raised in [K. Zietak, 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 -Birkhoff orthogonality with respect to the Ky Fan p-k norm are also derived.
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