The Hahn-Banach Theorem and Optimization Problems
The Hahn-Banach theorem is the most important theorem about the structure of linear continuous functionals on normed spaces. In terms of geometry, the Hahn-Banach theorem guarantees the separation of convex sets in normed spaces by hyperplanes. Figure 1.1 describes a number of important consequences of the Hahn-Banach theorem that will be studied in this chapter and the following one.
KeywordsBanach Space Topological Space Normed Space Dual Problem Linear Subspace
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