関数解析（テキスト） Functional Analysis

Vaidyanathan, Prahlad

Cambridge University Press（2023/09発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 300 p.
• 言語 ENG
• 商品コード 9781009243902
• DDC分類 515.7

Full Description

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.

Contents

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.