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arXiv · 2403.06445

On infinite matrices

Alexander Vasilyev·Vladimir Vasilyev·Abu Bakarr Kamanda Bongay
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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.

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Alexander Vasilyev, Vladimir Vasilyev, Abu Bakarr Kamanda Bongay. 2024-03-11. On infinite matrices. https://arxiv.org/abs/2403.06445

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