L-Matrices as Operators from ell_p to ell_q [r-libre/4154]

Bouthat, Ludovick, Mashreghi, Javad et Morneau-Guérin, Frédéric ORCID: https://orcid.org/0000-0001-7610-4648 (01 juin 2026). L-Matrices as Operators from ell_p to ell_q (sur invitation), présentée au Séminaire d'analyse, Lille, France.

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Catégorie de document :	Communications à des congrès/colloques et conférences (non publiées)
Évaluation par un comité de lecture :	Oui
Étape de publication :	Non publié
Résumé :	The Hadamard product of two power series is defined by coefficientwise multiplication. In 2020, Mashreghi and Ransford characterized the power series that act as Hadamard multipliers on all weighted Dirichlet spaces on the disk with superharmonic weight: these are precisely those whose associated $L$-matrix defines a bounded operator on $\\ell^2$. An $L$-matrix is an infinite matrix $L$ with entries $L\_{i,j} = a\_{\\max\\{i,j\\}}$ for a sequence $(a\_n)\_{n\\geq 0}$. In this talk, we characterize the sequences and we provide several convenient conditions ensuring that $L$ is a bounded operator on $\\ell^2$. We also identify a class of $L$-matrices, the Hilbert $L$-matrices, for which the operator norm can be computed exactly. Lastly, we present recent work in which these questions are extended to the more general case of operators from $\\ell^p$ to $\\ell^q$, for any $1\\leq p,q \\leq \\infty$.
Déposant:	Morneau-Guérin, Frédéric
Responsable :	Frédéric Morneau-Guérin
Dépôt :	30 juin 2026 17:14
Dernière modification :	30 juin 2026 17:14

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