English

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}
}
R2 v1 2026-06-28T19:44:38.386Z