Hilbert Spaces

Course in Functional Analysis - Conway

DSA ADS Course - 2021

A Course in Functional Analysis - Conway

Conway spells out the notion of a strict inductive limit of locally convex spaces, which is the only systematic way of talking about test functions and distributions. Chapter V, on weak topologies, is excellent, and proves, for example, the Banach-Alaoglu theorem, the Krein-Milman theorem, and proves (following de Branges) the Stone-Weierstrass theorem using the Krein-Milman theorem.