Banach’s Continuous Inverse Theorem and Closed Graph Theorem
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.
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Online Access: | https://doi.org/10.2478/v10037-012-0032-y |
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doaj-33a720ebf2ce49ab9675d5dc34c6f2672021-09-05T18:16:48ZengSciendoFormalized Mathematics1426-26301898-99342012-12-0120427127410.2478/v10037-012-0032-yBanach’s Continuous Inverse Theorem and Closed Graph TheoremSakurai Hideki0Okazaki Hiroyuki1Shidama Yasunari2406-3, Haneo, Naganohara Agatuma, Gunma, JapanShinshu University, Nagano, JapanShinshu University, Nagano, JapanIn 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.https://doi.org/10.2478/v10037-012-0032-y |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Sakurai Hideki Okazaki Hiroyuki Shidama Yasunari |
spellingShingle |
Sakurai Hideki Okazaki Hiroyuki Shidama Yasunari Banach’s Continuous Inverse Theorem and Closed Graph Theorem Formalized Mathematics |
author_facet |
Sakurai Hideki Okazaki Hiroyuki Shidama Yasunari |
author_sort |
Sakurai Hideki |
title |
Banach’s Continuous Inverse Theorem and Closed Graph Theorem |
title_short |
Banach’s Continuous Inverse Theorem and Closed Graph Theorem |
title_full |
Banach’s Continuous Inverse Theorem and Closed Graph Theorem |
title_fullStr |
Banach’s Continuous Inverse Theorem and Closed Graph Theorem |
title_full_unstemmed |
Banach’s Continuous Inverse Theorem and Closed Graph Theorem |
title_sort |
banach’s continuous inverse theorem and closed graph theorem |
publisher |
Sciendo |
series |
Formalized Mathematics |
issn |
1426-2630 1898-9934 |
publishDate |
2012-12-01 |
description |
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. |
url |
https://doi.org/10.2478/v10037-012-0032-y |
work_keys_str_mv |
AT sakuraihideki banachscontinuousinversetheoremandclosedgraphtheorem AT okazakihiroyuki banachscontinuousinversetheoremandclosedgraphtheorem AT shidamayasunari banachscontinuousinversetheoremandclosedgraphtheorem |
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1717786036983037952 |