A simple proof of the closed graph theorem
Functional Analysis
2016-01-13 v1
Abstract
Assume that is a closed linear operator defined on all of a Hilbert space . Then 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.
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}
}