Fundamentals of Functional Analysis 01

Abstract

This course introduces the main concepts and fundamental results of Functional Analysis for first-year Master’s (M1) students at the University of M’sila. It covers normed and Banach spaces, Hilbert spaces, continuous linear operators, and dual spaces. Special emphasis is placed on the fundamental theorems of the theory, including the Hahn–Banach Theorem, the Uniform Boundedness Principle, the Open Mapping Theorem, and the Closed Graph Theorem. The course also presents weak topologies and weak convergence, highlighting their importance in operator theory and applications.