Introduction to Banach Spaces and Algebras

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Graham Allan (University of Cambridge [Deceased 2007]) H. Garth Dales (University of Leeds)

Introduction to Banach Spaces and Algebras

Graham Allan (University of Cambridge [Deceased 2007]), H. Garth Dales (University of Leeds)

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English

Oxford University Press
20 November 2010

Algebra; Real analysis, real variables; Complex analysis, complex variables; Analytic topology

Series: Oxford Graduate Texts in Mathematics

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.

By: Graham Allan (University of Cambridge [Deceased 2007])
Edited by: H. Garth Dales (University of Leeds)
Imprint: Oxford University Press
Country of Publication: United Kingdom
Volume: 20
Dimensions: Height: 240mm, Width: 163mm, Spine: 27mm
Weight: 708g
ISBN: 9780199206537
ISBN 10: 0199206538
Series: Oxford Graduate Texts in Mathematics
Pages: 380
Publication Date: 20 November 2010
Audience: College/higher education , A / AS level , Further / Higher Education
Format: Hardback
Publisher's Status: Active

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.

Reviews for Introduction to Banach Spaces and Algebras

This well-crafted and scholarly book ...leaves nothing to be desired: this is a fine way to get into this beautiful in a subject and will serve to reel in a huge number of futureews devotees. * Michael Berg, MAA Reviews *