English

A simple proof of the closed graph theorem

Functional Analysis 2016-01-13 v1

Abstract

Assume that AA is a closed linear operator defined on all of a Hilbert space HH. Then AA is bounded. A new short proof of this classical theorem is given on the basis of the uniform boundedness principle. The proof can be easily extended to Banach spaces.

Keywords

Cite

@article{arxiv.1601.02600,
  title  = {A simple proof of the closed graph theorem},
  author = {A. G. Ramm},
  journal= {arXiv preprint arXiv:1601.02600},
  year   = {2016}
}
R2 v1 2026-06-22T12:27:10.554Z