In this article we formalize one of the most important theorems of linear operator theory - the Closed Graph Theorem commonly used in a standard text book such as [10] in Chapter 24.3. It states that a surjective closed linear operator between Banach spaces is bounded.
@article{bwmeta1.element.doi-10_2478_v10037-012-0032-y,
author = {Hideki Sakurai and Hiroyuki Okazaki and Yasunari Shidama},
title = {Banach's Continuous Inverse Theorem and Closed Graph Theorem},
journal = {Formalized Mathematics},
volume = {20},
year = {2012},
pages = {271-274},
zbl = {1283.46004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10037-012-0032-y}
}
Hideki Sakurai; Hiroyuki Okazaki; Yasunari Shidama. Banach’s Continuous Inverse Theorem and Closed Graph Theorem. Formalized Mathematics, Tome 20 (2012) pp. 271-274. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10037-012-0032-y/
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