Functional Analysis

This textbook guides graduate students and researchers through the basics of Functional Analysis and the theory of Operator Algebras.

Prahlad Vaidyanathan (Author)

9781009243902, Cambridge University Press

Paperback / softback, published 21 September 2023

300 pages
24.1 x 18.4 x 2.3 cm, 0.73 kg

Since its inception in the early 20th century, Functional Analysis has become a core part of modern mathematics. This accessible and lucid textbook will guide students through the basics of Functional Analysis and the theory of Operator Algebras. The text begins with a review of Linear Algebra and Measure Theory. It progresses to concepts like Banach spaces, Hilbert spaces, Dual spaces and Weak Topologies. Subsequent chapters introduce the theory of operator algebras as a guide to study linear operators on a Hilbert space and cover topics such as Spectral Theory and C*-algebras. Theorems have been introduced and explained through proofs and examples, and historical background to the mathematical concepts have been provided wherever appropriate. At the end of chapters, practice exercises have been segregated in a topic-wise manner for targeted practice, making the book ideal both for classroom teaching as well as self-study.

Preface
Notation
1. Preliminaries
2. Normed Linear Spaces
3. Hilbert Spaces
4. Dual Spaces
5. Operators on Banach Spaces
6. Weak Topologies
7. Spectral Theory
8. C*-Algebras
9. Measure and Integration
10. Normal Operators on Hilbert Spaces
Appendices
A.1 The Stone–Weierstrass Theorem
A.2 The Radon–Nikodym Theorem
Bibliography
Index.

Subject Areas: Calculus & mathematical analysis [PBK]