This book is based on courses taught by the author at Moscow State University. Compared to many other books on the subject, it is unique in that the exposition is based on extensive use of the language and elementary constructions of category theory. Among topics featured in the book are the theory of Banach and Hilbert tensor products, the theory of distributions and weak topologies, and Borel operator calculus. The book contains many examples illustrating the general theory presented, as well as multiple exercises that help the reader to learn the subject. It can be used as a textbook on selected topics of functional analysis and operator theory. Prerequisites include linear algebra, elements of real analysis, and elements of the theory of metric spaces.
Foundations: Categories and the like Normed spaces and bounded operators ("Waiting for completeness") Banach spaces and their advantages From compact spaces to Fredholm operators Polynormed spaces, weak topologies, and generalized functions At the gates of spectral theory Hilbert adjoint operators and the spectral theorem Fourier transform Bibliography Index.