Banach’s Continuous Inverse Theorem and Closed Graph Theorem

Hideki Sakurai 1 , Hiroyuki Okazaki 2 , and Yasunari Shidama 2
  • 1 406-3, Haneo, Naganohara Agatuma, Gunma, Japan
  • 2 Shinshu University, Nagano, Japan

Summary

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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