Hereditarily and nonhereditarily complete systems of vectors in a Hilbert space

2025/05/21 by Prokofyev, Mikhail
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2505.15321

Abstract

In this paper, we study the property of hereditary completeness of vector systems \x_k\_k=1^∞ 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 ∈ N}, N ⊂ 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.

Citations

• On k point density problem for band-diagonal M-bases
• Spectral synthesis in de Branges spaces
• Hereditary completeness for systems of exponentials and reproducing kernels

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