Abstract
The main consequences of completeness for Banach spaces are discussed, including the Banach-Steinhaus theorem, uniform boundedness, and an application to Fourier series. The open mapping and closed graph theorems are proved, along with some of their consequences.
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© 2017 Springer International Publishing AG
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Einsiedler, M., Ward, T. (2017). Uniform Boundedness and the Open Mapping Theorem. In: Functional Analysis, Spectral Theory, and Applications. Graduate Texts in Mathematics, vol 276. Springer, Cham. https://doi.org/10.1007/978-3-319-58540-6_4
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DOI: https://doi.org/10.1007/978-3-319-58540-6_4
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-58539-0
Online ISBN: 978-3-319-58540-6
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