English

A note on Basis Problem in normed spaces

Functional Analysis 2024-11-06 v5

Abstract

In this work, we prove the criterion of Banach-Grunblum and the principle of selection of Bessaga-Pe\l{}czy\'nski for normed spaces. As applications of these results, we show the Principle of Selection of Bessaga-Pe\l{}czy\'nski for normed spaces and the Spectral Theorem for compact self-adjoint operators on inner product spaces.

Keywords

Cite

@article{arxiv.1806.07943,
  title  = {A note on Basis Problem in normed spaces},
  author = {Vinicius Coelho and Joilson Ribeiro and Luciana Salgado},
  journal= {arXiv preprint arXiv:1806.07943},
  year   = {2024}
}

Comments

17 pages. Improvement of the paper, added a section of conclusion, including a Spectral Theorem in this context, new references, deleted some references not used in the text. To b published in EQUATIONS, An Open Access International Journal of Mathematical and Computational Methods in Science and Engineering. No fees have been paid for this publication

R2 v1 2026-06-23T02:36:33.353Z