 BROWSE
 USED
 STAFF PICKS
 GIFTS + GIFT CARDS
 SELL BOOKS
 BLOG
 EVENTS
 FIND A STORE
 800.878.7323

On Order
$76.25
New Trade Paper
Currently out of stock.
available for shipping or prepaid pickup only
This title in other editionsOther titles in the Oxford Graduate Texts in Mathematics series:
Oxford Graduate Texts in Mathematics #20: Introduction to Banach Spaces and Algebrasby Graham R. Allan
Synopses & ReviewsPublisher 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 BanachAlaoglu, HahnBanach, 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 AuthorGraham 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 NewcastleuponTyne, 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 ViceMaster of the College 199093.
Table of ContentsPART 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 What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
Related Subjects
Health and SelfHelp » Health and Medicine » Nursing


