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Oxford Graduate Texts in Mathematics #20: Introduction to Banach Spaces and Algebras

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Oxford Graduate Texts in Mathematics #20: Introduction to Banach Spaces and Algebras Cover

 

Synopses & Reviews

Publisher Comments:

Banach spaces and algebras are a key topic of pure mathematics. Graham Allan's careful and detailed introductory account will prove essential reading for anyone wishing to specialise in functional analysis and is aimed at final year undergraduates or masters level students. Based on the author's lectures to fourth year students at Cambridge University, the book assumes knowledge typical of first degrees in mathematics, including metric spaces, analytic topology, and complex analysis. However, readers are not expected to be familiar with the Lebesgue theory of measure and integration.

The text begins by giving the basic theory of Banach spaces, including dual spaces and bounded linear operators. It establishes forms of the theorems that are the pillars of functional analysis, including the Banach-Alaoglu, Hahn-Banach, uniform boundedness, open mapping, and closed graph theorems. There are applications to Fourier series and operators on Hilbert spaces.

The main body of the text is an introduction to the theory of Banach algebras. A particular feature is the detailed account of the holomorphic functional calculus in one and several variables; all necessary background theory in one and several complex variables is fully explained, with many examples and applications considered. Throughout, exercises at sections ends help readers test their understanding, while extensive notes point to more advanced topics and sources.

The book was edited for publication by Professor H. G. Dales of Leeds University, following the death of the author in August, 2007.

About the Author

Graham Allan was a student of mathematics at Cambridge University, England, and obtained his PhD there in 1964. After periods as a Fellow at Cambridge, as a lecturer at the University of Newcastle-upon-Tyne, and as Professor of Pure Mathematics at the University of Leeds, Graham returned to Cambridge as a lecturer in mathematics in 1978, and he became a Reader in Functional Analysis in 1980. Graham was a Fellow of Churchill College from 1978, Director of Studies in Mathematics from 1985, and Vice-Master of the College 1990-93.

Table of Contents

PART I INTRODUCTION TO BANACH SPACES

1. Preliminaries

2. Elements of normed spaces

3. Banach spaces

PART II BANACH ALGEBRAS

4. Banach algebras

5. Representation theory

6. Algebras with an involution

7. The Borel functional calculus

PART III SCV AND BANACH ALGEBRAS

8. Introduction to several complex variables

9. The holomorphic functional calculus in several variables

Bibliography

Index

Product Details

ISBN:
9780199206544
Author:
Allan, Graham R.
Publisher:
Oxford University Press, USA
Author:
null, H. Garth
Author:
null, Graham
Author:
Dales, H. Garth
Author:
Allan, Graham
Subject:
Functional Analysis
Subject:
Mathematics | Pure Mathematics
Subject:
Mathematics : Functional Analysis
Series:
Oxford Graduate Texts in Mathematics
Series Volume:
20
Publication Date:
20101231
Binding:
TRADE PAPER
Grade Level:
Professional and scholarly
Language:
English
Illustrations:
none
Pages:
384
Dimensions:
6.1 x 9.2 x 0.9 in 1.3 lb

Related Subjects

Health and Self-Help » Health and Medicine » Nursing
Science and Mathematics » Chemistry » General
Science and Mathematics » Mathematics » Functional Analysis
Science and Mathematics » Mathematics » General

Oxford Graduate Texts in Mathematics #20: Introduction to Banach Spaces and Algebras New Trade Paper
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