Morneau-Guérin, Frédéric 
ORCID: https://orcid.org/0000-0001-7610-4648
(sous presse).
Two-valued maximizing vectors and the l^p Chebyshev radius of the Birkhoff polytope. Canadian Mathematical Bulletin.
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- Two-valued maximizing vectors.pdf
Contenu du fichier : Manuscrit accepté (révisé après évaluation) Accès restreint jusqu'à fin- janvier 2027. |
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| Catégorie de document : | Articles de revues |
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| Évaluation par un comité de lecture : | Oui |
| Étape de publication : | Accepté (sous presse) |
| Résumé : | Let A(n,-a,b) be the n by n matrix with diagonal entries -a and off-diagonal entries b, where a greater or equal to 0 and b>0, acting on l^p_n$. We prove that for every n greater or equal to 3 and every 1<p< infinity with p not equal to 2, each real vector at which A(n,-a,b) attains its operator norm has at most two distinct coordinates. This is the nondegenerate case of a conjecture of Bouthat, Mashreghi and Morneau-Gu\'erin; the remaining boundary cases of that conjecture are either elementary or false, and we point out the exceptions. As a consequence we obtain an explicit formula for the Chebyshev radius of the Birkhoff polytope with respect to the l_n^p$ operator norm, which settles in full a second conjecture of the same authors. The proof shows that the coordinates of a norm-attaining vector are roots of one scalar equation, then uses the second-order condition for a maximum, together with an exact identity, to rule out three distinct roots. |
| Déposant: | Morneau-Guérin, Frédéric |
| Responsable : | Frédéric Morneau-Guérin |
| Dépôt : | 16 sept. 2026 14:56 |
| Dernière modification : | 21 sept. 2026 23:22 |
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