English

Characterizing Riesz Bases via Biorthogonal Riesz-Fischer sequences

Functional Analysis 2022-12-06 v1

Abstract

In this note we prove that if two Riesz-Fischer sequences in a separable Hilbert space HH are biorthogonal and one of them is complete in HH, then both sequences are Riesz bases for HH. This complements a recent result by D. T. Stoeva where the same conclusion holds if one replaces the phrase ``Riesz-Fischer sequences'' by ``Bessel sequences''.

Cite

@article{arxiv.2212.02252,
  title  = {Characterizing Riesz Bases via Biorthogonal Riesz-Fischer sequences},
  author = {Elias Zikkos},
  journal= {arXiv preprint arXiv:2212.02252},
  year   = {2022}
}
R2 v1 2026-06-28T07:22:24.149Z