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Bibliographic Details
Main Author: Prokofyev, Mikhail
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2505.15321
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Table of 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.