Kutateladze S.S. Fundamentals of Functional Analysis

Textbook. — Dordrecht: Kluwer Academic Publishers, 1995. — xii+275 p.This is a concise guide to basic sections of modern functional analysis. Included are such topics as the principles of Banach and Hilbert spaces, the theory of multi-normed and uniform spaces, the Riesz–Dunford holomorphic functional calculus, the Fredholm index theory, convex analysis and duality theory for locally convex spaces.
With standard provisos the presentation is self-sufficient, whereas exposing about a hundred of celebrated named theorems furnished with complete proofs and culminating in the Gelfand–Na˘ımark–Segal construction for C ∗ -algebras.
The first Russian edition was printed by the Siberian Division of the Nauka Publishers in 1983. Since then the monograph has served as the standard textbook on functional analysis at the University of Novosibirsk.