A Course on Topological Vector Spaces

The book delves into the theory of topological vector spaces, emphasizing locally convex spaces. It explores topologies in dual pairs and presents significant results such as the Mackey-Arens theorem. Key properties of weak topology on Banach spaces are examined, including Banach's theorem regarding weak*-closed subspaces, the Eberlein-Smulian theorem, Krein's insights on weakly compact sets, and the Dunford-Pettis theorem that defines weak compactness. This comprehensive approach offers valuable insights for advanced studies in functional analysis.