On Schauder Bases in Hilbert Space
Functional Analysis
2024-11-08 v3 Mathematical Physics
math.MP
Abstract
In this short note we present a far generalization of the following very well-known assertion: assume that we have two orthonormal sequences in a Hilbert space and these sequences are quadratically close to each other. Then if one of these sequences is a basis in the Hilbert space then so is the other one.
Keywords
Cite
@article{arxiv.2411.00797,
title = {On Schauder Bases in Hilbert Space},
author = {Oleg Zubelevich},
journal= {arXiv preprint arXiv:2411.00797},
year = {2024}
}