On infinite matrices
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909133745160192 |
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| author | Vasilyev, Alexander Vasilyev, Vladimir Bongay, Abu Bakarr Kamanda |
| author_facet | Vasilyev, Alexander Vasilyev, Vladimir Bongay, Abu Bakarr Kamanda |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_06445 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On infinite matrices Vasilyev, Alexander Vasilyev, Vladimir Bongay, Abu Bakarr Kamanda Functional Analysis Numerical Analysis 47B01, 65N22 F.2.1 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. |
| title | On infinite matrices |
| topic | Functional Analysis Numerical Analysis 47B01, 65N22 F.2.1 |
| url | https://arxiv.org/abs/2403.06445 |