This module introduces the theory of Banach spaces and their applications.
*Curricular information is subject to change
Normed spaces: definition, basic properties and examples. Banach spaces; finite- dimensional Banach spaces, continuous linear functionals on Banach spaces.
Hahn-Banach Theorem. Separation Theorem and its applications in economics and in classification theory. Farcas' Lemma and its applications to linear programming.
Continuous linear operators on Banach spaces, examples (differentiation, integral transforms). Norm of an operator, spaces of operators. Open mapping and closed graph theorems.
Lectures supported by tutorials
| Module Content & Assessment | |
|---|---|
| Assessment Breakdown | % |
| Formal Examination | 100 |