Abstract
The Hahn-Banach theorem, in the geometrical form, states that a closed and convex set can be separated from any external point by means of a hyperplane. This intuitively appealing principle underlines the role of convexity in the theory. It is the first, and most important, of the fundamental principles of functional analysis. The rich duality theory of Banach spaces is one of its direct consequences. The second fundamental principle, the Banach open mapping theorem, is studied in the rest of the chapter.
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References
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Fabian, M., Habala, P., Hájek, P., Montesinos, V., Zizler, V. (2011). Hahn–Banach and Banach Open Mapping Theorems. In: Banach Space Theory. CMS Books in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7515-7_2
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DOI: https://doi.org/10.1007/978-1-4419-7515-7_2
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