Open access research
publication repository
publication repository
Bouthat, Ludovick; Mashreghi, Javad, & Morneau-Guérin, Frédéric (Dec 2020). The norm of an infinite L-matrix. Paper presented at the Réunion d'hiver de la Société Mathématique du Canada 2020, Montréal.
File(s) available for this item:|
PDF
- The norm of an infinite L-matrix - CMS winter meeting 2020.pdf
Content : Slideshow Restricted access till end- January 2026. |
|
| Item Type: | Conference papers (unpublished) |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| Status: | Unpublished |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 times 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 will use the Schur test to find some conditions on the sequence (a_n) for A to be an operator on l2 and to find an upper bound on the l2 norm of A. Moreover, we will use these tools to find the exact norm of a particular set of L-matrices. |
| Official URL: | https://www2.cms.math.ca/Events/Winter20/ |
| Depositor: | Morneau-Guérin, Frédéric |
| Owner / Manager: | Frédéric Morneau-Guérin |
| Deposited: | 30 Jan 2025 13:49 |
| Last Modified: | 30 Mar 2025 13:49 |
|
RÉVISER |
