TL;DR
This paper proves that any non-complete orthonormal system in a Hilbert space can be converted into a basis through small perturbations, providing a method to enhance basis completeness.
Contribution
It introduces a novel approach to transforming non-complete orthonormal systems into bases via small perturbations in Hilbert spaces.
Findings
Non-complete systems can be made complete with perturbations
Small perturbations can transform systems into bases
The method applies generally in Hilbert spaces
Abstract
We prove that any non-complete orthonormal system in a Hilbert space can be transformed into a basis by small perturbations.
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Taxonomy
TopicsQuantum chaos and dynamical systems · Matrix Theory and Algorithms · Spectral Theory in Mathematical Physics