On infinite matrices
<|reference_start|>On infinite matrices: 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.<|reference_end|>
@article{vasilyev2024on,
    title={On infinite matrices},
    author={Alexander Vasilyev, Vladimir Vasilyev and Abu Bakarr Kamanda Bongay},
    journal={arXiv preprint arXiv:2403.06445},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.06445},
    primaryClass={math.FA cs.NA math.NA}
}