Course abstract

Functional Analysis is a core course in any mathematics curriculum at the masters level. It has wide ranging applications in several areas of mathematics, especially in the modern approach to the study of partial differential equations. The proposed course will cover all the material usually dealt with in any basic course of Functional Analysis. Starting from normed linear spaces, we will study all the important theorems, with applications, in the theory of Banach and Hilbert spaces. One important feature of the proposed course is the detailed treatment of weak topologies. Prerequisites are familiarity with real analysis, topology and linear algebra. Knowledge of measure theory is desirable.