Vitali D. Milman

Antonis Tsolomitis

Yuli Eidelman

The goal of this textbook is to provide an introduction to the methods and language of functional analysis, including Hilbert spaces, Fredholm theory for compact operators, and spectral theory of self-adjoint operators. It also presents the basic theorems and methods of abstract functional analysis and a few applications of these methods to Banach algebras and the theory of unbounded self-adjoint operators. The text corresponds to material for two semester courses (Part I and Part II, respectively), and it is as self-contained as possible. The only prerequisites for the first part are minimal amounts of linear algebra and calculus. However, for the second course (Part II), it is useful to have some knowledge of topology and measure theory. Each chapter is followed by numerous exercises, whose solutions are given at the end of the book.

An Introduction

Functional Analysis

Apostolos Syropoulos

Nick Sofroniou

Using clear and concise language this book introduces new users to the use of the TeX system, in particular document preparation using LaTeX. It avoids the pitfalls of having to search through several advanced books on the subject, by collecting together the more frequently required tools and presenting these in a single accessible volume. It also describes the recent developments in multilingual typesetting using TeX that now make it straightforward for users to prepare documents in their own language and alphabet, giving the book a global readership. Topics include: multi-lingual uses of LaTeX; discussion of hardware implementations; use and misuse of particular LaTeX commands; and many others.

Antonis Tsolomitis

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