In this article at first, we proved the lemma of the inferior limit and the superior limit. Next, we proved the Baire category theorem (Banach space version) [20], [9], [3], quoted it and proved the uniform boundedness principle. Moreover, the proof of the Banach-Steinhaus theorem is added.MML identifier: LOPBAN 5, version: 7.8.05 4.89.993
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.
In this article we formalize one of the most important theorems of linear operator theory the Open Mapping Theorem commonly used in a standard book such as [8] in chapter 2.4.2. It states that a surjective continuous linear operator between Banach spaces is an open map.MML identifier: LOPBAN 6, version: 7.10.01 4.111.1036
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