Banach’s Continuous Inverse Theorem and Closed Graph Theorem

Hideki Sakurai; Hiroyuki Okazaki; Yasunari Shidama

Formalized Mathematics (2012)

  • Volume: 20, Issue: 4, page 271-274
  • ISSN: 1426-2630

Abstract

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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.

How to cite

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Hideki Sakurai, Hiroyuki Okazaki, and Yasunari Shidama. "Banach’s Continuous Inverse Theorem and Closed Graph Theorem." Formalized Mathematics 20.4 (2012): 271-274. <http://eudml.org/doc/267765>.

@article{HidekiSakurai2012,
abstract = {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.},
author = {Hideki Sakurai, Hiroyuki Okazaki, Yasunari Shidama},
journal = {Formalized Mathematics},
language = {eng},
number = {4},
pages = {271-274},
title = {Banach’s Continuous Inverse Theorem and Closed Graph Theorem},
url = {http://eudml.org/doc/267765},
volume = {20},
year = {2012},
}

TY - JOUR
AU - Hideki Sakurai
AU - Hiroyuki Okazaki
AU - Yasunari Shidama
TI - Banach’s Continuous Inverse Theorem and Closed Graph Theorem
JO - Formalized Mathematics
PY - 2012
VL - 20
IS - 4
SP - 271
EP - 274
AB - 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.
LA - eng
UR - http://eudml.org/doc/267765
ER -

References

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