Some results about infinite L-matrices [r-libre/3573]

Bouthat, Ludovick; Mashreghi, Javad, & Morneau-Guérin, Frédéric (Jun 2021). Some results about infinite L-matrices. Paper presented at the Réunion d'été de la Société Mathématique du Canada 2021.

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Item Type:	Conference papers (unpublished)
Refereed:	Yes
Status:	Unpublished
Abstract:	We know that any linear application from Cn to Cn can be described with an n x n square matrix. The space l2 of square-summable sequences indexed by the natural numbers is a generalization of Cn to infinite dimension. We find that the operators, in the case of l2, can be described by infinite matrices. However, not all infinite matrices gives us an operator on l2. It is natural to wonder which infinite matrices are a representation of an operator on l2, and what is their norm. Because of their applications in the problem of the caracterisation of the multipliers in the weighted Dirichlet spaces, we restrict ourselves to the case of infinite L-matrices. An infinite positive L-matrix is an infinite matrix which is defined by a sequence (a_n) of positive real numbers and which is of a prescribed form. We present some conditions on the sequence (a_n) forA to be an operator on l2 and we present a particular set of L-matrices for which we are able to exactly determine the norm. We also show some new results about L-matrices with lacunary coefficients.
Official URL:	https://summer21.cms.math.ca/
Depositor:	Morneau-Guérin, Frédéric
Owner / Manager:	Frédéric Morneau-Guérin
Deposited:	30 Jan 2025 20:47
Last Modified:	30 Mar 2025 13:51

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