Introduction to Banach Spaces and Algebras (Oxford Graduate Texts in Mathematics)

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9780199206544: Introduction to Banach Spaces and Algebras (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.

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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.

Review:

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

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Graham Allan
Editorial: Oxford University Press, United Kingdom (2010)
ISBN 10: 0199206546 ISBN 13: 9780199206544
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Descripción Oxford University Press, United Kingdom, 2010. Paperback. Estado de conservación: New. Language: English . Brand New Book. 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. Nº de ref. de la librería AOP9780199206544

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Graham Allan
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Descripción Oxford University Press, United Kingdom, 2010. Paperback. Estado de conservación: New. Language: English . Brand New Book. 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. Nº de ref. de la librería AOP9780199206544

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Descripción 2010. PAP. Estado de conservación: New. New Book. Shipped from US within 10 to 14 business days. Established seller since 2000. Nº de ref. de la librería VU-9780199206544

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Descripción OUP Oxford, 2010. PAP. Estado de conservación: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Nº de ref. de la librería FU-9780199206544

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Descripción Oxford University Press, 2010. Paperback. Estado de conservación: New. book. Nº de ref. de la librería M0199206546

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Descripción Oxford Univ Pr, 2010. Paperback. Estado de conservación: Brand New. 1st edition. 384 pages. 9.25x6.25x1.00 inches. In Stock. Nº de ref. de la librería __0199206546

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Descripción Oxford University Press, USA, 2010. Paperback. Estado de conservación: New. 1. Nº de ref. de la librería DADAX0199206546

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