Functional analysis [SMATB301]

Learning outcomes

The aim of the course is to study the important theorems of Fonctional Analysis in the framework of normed spaces of infinite dimension and to apply them to the solution of linear functional equations.

Content

Linear and bounded operators. Hahn-Banach theorems, separation of convex sets, Banach-Steinhaus theorem. Open mapping theorem and closed graph theorem. After that the weak and weak-* topologies are studied (Banach-Alaoglu theorem and reflexiive spaces). The second part of the course is devoted to the spectral theory of compact operators (Neumann lemma, Fredholm Alternative theorems. Finally the obtained results are applied for solving integral equations in the framework of Hilbert spaces.