Hideki Sakurai, Hiroyuki Okazaki, Yasunari Shidama
Abstract
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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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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.
Key concepts: Closed graph theorem, Mathematics, Bounded inverse theorem, Unbounded operator, Discrete mathematics, Open mapping theorem (functional analysis), Eberlein–Šmulian theorem, Finite-rank operator