Introduction to Banach Spaces and Algebras

Paperback | December 4, 2010

byGraham Allan

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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 theauthor'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 andintegration.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 examplesand 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.

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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 theauthor's lectures to fourth year students at Cambr...

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 197...

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Format:PaperbackDimensions:384 pages, 9.21 × 6.14 × 0.87 inPublished:December 4, 2010Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0199206546

ISBN - 13:9780199206544

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Table of Contents

PART I Introduction to Banach Spaces1. Preliminaries2. Elements of normed spaces3. Banach spacesPART II Banach Algebras4. Banach algebras5. Representation theory6. Algebras with an involution7. The Borel functional calculusPART III SCV and Banach Algebras8. Introduction to several complex variables9. The holomorphic functional calculus in several variablesBibliographyIndex