Properties of best approximations with respect to the Ky Fan p-k norm, and the strict spectral approximant of a matrix [r-libre/4158]

Morneau-Guérin, Frédéric ORCID: https://orcid.org/0000-0001-7610-4648 (2026). Properties of best approximations with respect to the Ky Fan p-k norm, and the strict spectral approximant of a matrix [compte rendu de l'ouvrage de Grover, Priyanka et Gupta, Krishna Kumar]. zbMATH Open.

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Catégorie de document :	Comptes rendus d'ouvrages
Évaluation par un comité de lecture :	Oui
Étape de publication :	Publié
Résumé :	The main contribution of the paper is an explicit description of the subdifferential of the Ky Fan p-k norms for p in 2,infinity). Using this description, the authors obtain characterizations of best approximations, Birkhoff-James rthogonality, epsilon-Birkhoff orthogonality, norm parallelism, and orthogonality to linear subspaces with respect to these norms. The authors also prove uniqueness of best approximations to one-dimensional subspaces under suitable rank assumptions and obtain partial results on the convergence of Ky Fan p-k approximations to the strict spectral approximation, thereby answering several questions raised by Ziȩtak. The arguments combine techniques from convex analysis, subdifferential calculus, Fréchet differentiation of matrix functions, and the theory of unitarily invariant norms.
Adresse de la version officielle :	https://zbmath.org/08213463
Déposant:	Morneau-Guérin, Frédéric
Responsable :	Frédéric Morneau-Guérin
Dépôt :	08 juill. 2026 19:29
Dernière modification :	08 juill. 2026 19:29

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