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arXiv · 2505.15321

Hereditarily and nonhereditarily complete systems of vectors in a Hilbert space

Mikhail Prokofyev
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Abstract

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.

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Mikhail Prokofyev. 2025-05-21. Hereditarily and nonhereditarily complete systems of vectors in a Hilbert space. https://arxiv.org/abs/2505.15321

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