On infinite matrices
Functional Analysis
2024-03-12 v1 Numerical Analysis
Numerical Analysis
Abstract
We consider linear bounded operators acting in Banach spaces with a basis, such operators can be represented by an infinite matrix. We prove that for an invertible operator there exists a sequence of invertible finite-dimensional operators so that the family of norms of their inverses is uniformly bounded. It leads to the fact that solutions of finite-dimensional equations converge to the solution of initial operator equation with infinite-dimensional matrix.
Cite
@article{arxiv.2403.06445,
title = {On infinite matrices},
author = {Alexander Vasilyev and Vladimir Vasilyev and Abu Bakarr Kamanda Bongay},
journal= {arXiv preprint arXiv:2403.06445},
year = {2024}
}
Comments
7 pages