Functional analysis
Material type: TextPublication details: Cambridge : Cambridge University Press, ©2023.Description: xi, 543 p. : ill. ; 24 cmISBN:- 9781009243902
- 515.7 23/eng20230919 VAI-F
- QA320 .V35 2023
- MAT034000
Item type | Current library | Collection | Call number | Status | Date due | Barcode | Item holds |
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Books | IIITD General Stacks | Mathematics | 515.7 VAI-F (Browse shelf(Opens below)) | Available | 012804 |
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515.7 SOM-F A first course in functional analysis | 515.7 SUH-F Functional analysis | 515.7 TOR-P Problems in real and functional analysis | 515.7 VAI-F Functional analysis | 515.7 YAM-F From vector spaces to function spaces : introduction to functional analysis with applications | 515.7 YOS-F Functional analysis | 515.7223 PRA-R Representation theory : |
Includes bibliographical references and index.
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
"Functional Analysis is a part of mathematics that deals with linear spaces equipped with a topology. The subject began with the work of Fredholm, Hilbert, Banach and others in the early 20th century. They developed an algebraic/topological framework which could be used to address a variety of questions in analysis. The subject immediately saw connections to abstract algebra, partial differential equations, geometry and much more. This book is meant to introduce the reader to functional analysis. The first half of the book will cover the basic material that is taught in Masters programs across the world and prove all the major theorems in great detail. The second half of the book will focus on operators on a Hilbert space and is built around the proof of the spectral theorem - a central result in the subject that ties together traditional functional analysis with the modern theory of operator algebras. The book aims to provide an accessible, interesting and readable introduction to the subject. It will also take the reader a little further than most courses do by introducing them to the language of operator algebras. This will help future researchers by giving them a jumping off point as they dive into deeper books on the subject"--
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