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Functional Analysis: An Introduction
Yuli Eidelman, Vitali Milman, Antonis Tsolomitis
Price
1695.00
ISBN
9780821868799
Language
English
Pages
344
Format
Paperback
Dimensions
180 x 240 mm
Year of Publishing
2011
Territorial Rights
Restricted
Imprint
American Mathematical Society
Catalogues

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.

Yuli Eidelman and Vitali Milman, Tel Aviv University, Israel, and Antonis Tsolomitis, University of the Aegean, Samos, Greece.

Part I. Hilbert Spaces and Basic Operator Theory
  1. Linear Spaces; normed spaces; first examples
  2. Hilbert Spaces
  3. The dual space
  4. Bounded linear operators
  5. Spectrum. Fredholm theory of compact operations
  6. Self-adjoint operators
  7. Functions of operators; spectral decompositions
PART II. Basics of Functional Analysis
  1. Spectral theory of unitary operators
  2. The Fundamental theorems and the basic methods
  3. Banach algebras
  4. Unbounded self-adjoint and symmetric operators in H
Solutions to exercises
Bibliography
Symbols index
Subject index
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