Abstract
This chapter is devoted to five fundamental results of functional analysis, namely Hahn–Banach theorem, Banach–Alaoglu theorem, uniform boundedness principle, open mapping theorem, and closed graph theorem. These theorems have played significant role in approximation theory, Fourier analysis, numerical analysis, control theory, optimization, mechanics, mathematical economics, and differential and partial differential equations.
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Siddiqi, A.H. (2018). Fundamental Theorems. In: Functional Analysis and Applications. Industrial and Applied Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-10-3725-2_4
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DOI: https://doi.org/10.1007/978-981-10-3725-2_4
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Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-3724-5
Online ISBN: 978-981-10-3725-2
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