Fundamentals of Functional Analysis 01
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UNIVERSITE MOHAMED BOUDIAF –M’SILA
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.
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Keywords
Normed spaces, Banach spaces, Hilbert spaces, inner product, orthogonality, linear operators, bounded operators Continuous linear functionals, dual spaces, Hahn–Banach theorem, open Mapping theorem, closed Graph theorem, uniform Boundedness Principle, weak convergenc, weak-* convergence, reflexive spaces