Hereditarily and nonhereditarily complete systems of vectors in a Hilbert space
Abstract
In this paper, we study the property of hereditary completeness of vector systems \xk\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 \xk\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.
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