Functional Analysis: An Introduction Eidelman, Yuli, Milman, Vitali & Tsolomitis, Antonis

Functional Analysis: An Introduction

Eidelman, Yuli, Milman, Vitali & Tsolomitis, Antonis

2011; 344 pp; Paperback; 180 × 240 mm; 978-0-8218-6879-9

For sale only in India,Pakistan,Nepal,Bhutan,Bangladesh,Sri Lanka,Maldives

Series: Indian Editions of AMS Titles

755.00 This textbook provides 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 is essentially self-contained. Prerequisites for the first part are minimal amounts of linear algebra and calculus. For the second part, some knowledge of topology and measure theory is recommended. Each of the 11 chapters is followed by numerous exercises, with solutions given at the end of the book. The text is ideal for a one-year course. It will also provide a sound basis for further study. It is suitable for graduate students and researchers interested in operator theory and functional analysis. Part I. Hilbert Spaces and Basic Operator Theory Linear Spaces; normed spaces; first examples Hilbert Spaces The dual space Bounded linear operators Spectrum. Fredholm theory of compact operations Self-adjoint operators Functions of operators; spectral decompositions PART II. Basics of Functional Analysis Spectral theory of unitary operators The Fundamental theorems and the basic methods Banach algebras Unbounded self-adjoint and symmetric operators in H Solutions to exercises Bibliography Symbols index Subject index About the Author Yuli Eidelman and Vitali Milman, Tel Aviv University, Israel, and Antonis Tsolomitis, University of the Aegean, Samos, Greece