MA3G8 Functional Analysis Ii Notes | Assignment Help | Syllabus
Country: United Kingdom
University: The University Of Warwick
Problems presented in infinite-dimensional space appear often in mathematics, both pure and practical. The basic findings in the theory of infinite-dimensional Banach spaces (full normed linear spaces) and linear transformations between such spaces will be the focus of this subject.
We will prove some of the most important theorems about such linear spaces and their dual spaces (the space of all bounded linear functionals), such as the Hahn-Banach Theorem and the Principle of Uniform Boundedness, and show that, despite the fact that the unit ball is not compact in an infinite-dimensional space, the concept of weak convergence allows us to overcome this.
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