Title: CHAPTER 4. Some Major Theorems of Functional Analysis
Abstract: Publisher SummaryThis chapter discusses major theorems of functional analysis such as the Hahn–Banach theorem and its geometric equivalent, closed graph theorem, Banach inverse theorem, open-mapping theorem, and uniform boundedness theorem. It also discusses Holder's inequality-used extensively in manipulation of control problems in a concrete setting and norms on product spaces-required in the extension of results to spaces of higher dimension. The Hahn–Banach theorem is the fundamental tool to be used in establishing the existence of optimal controls. Mazur's theorem is the geometric version of the Hahn–Banach theorem. As the linear functionals can be identified with hyperplanes; accordingly, Mazur's theorem asserts the existence of a hyperplane. The theorem is often valuable in giving geometric insight.
Publication Year: 1980
Publication Date: 1980-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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