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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.15321 |
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| _version_ | 1866909618651791360 |
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| author | Prokofyev, Mikhail |
| author_facet | Prokofyev, Mikhail |
| contents | In this paper, we study the property of hereditary completeness of vector systems $\{x_k\}_{k=1}^\infty$ in a Hilbert space. A criterion of hereditary completeness is obtained in terms of projectors on closed linear spans of systems of the form $\{x_k\}_{k \in N}$, $N \subset \mathbb{N}$. Developed technique has been used to prove that mixed systems of a hereditarily complete system are also hereditarily complete. In conclusion, the problem of possible defects in a nonhereditarily complete system is considered. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_15321 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hereditarily and nonhereditarily complete systems of vectors in a Hilbert space Prokofyev, Mikhail Functional Analysis In this paper, we study the property of hereditary completeness of vector systems $\{x_k\}_{k=1}^\infty$ in a Hilbert space. A criterion of hereditary completeness is obtained in terms of projectors on closed linear spans of systems of the form $\{x_k\}_{k \in N}$, $N \subset \mathbb{N}$. Developed technique has been used to prove that mixed systems of a hereditarily complete system are also hereditarily complete. In conclusion, the problem of possible defects in a nonhereditarily complete system is considered. |
| title | Hereditarily and nonhereditarily complete systems of vectors in a Hilbert space |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2505.15321 |