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Introduction to Banach Spaces and Algebras

Introduction to Banach Spaces and Algebras (Hardback)

By Allan, Graham
Edited by Dales, H. Garth

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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 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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ISBN 9780199206537
Released NZ 20 Nov 2010
Publisher Oxford University Press (S3)
Format Hardback
Alternate Format(s) View All (1 other possible title(s) available)
Series Oxford Graduate Texts in Mathematics (part: 20)
Indent title (internationally sourced), usually ships 4-6 weeks

Full details for this title

ISBN-13 9780199206537
Stock Available
Status Indent title (internationally sourced), usually ships 4-6 weeks
Publisher Oxford University Press (S3)
Imprint Oxford University Press
Released 20 Nov 2010
Publication Country United Kingdom United Kingdom
Format Hardback
Author(s) By Allan, Graham
Edited by Dales, H. Garth
Series Oxford Graduate Texts in Mathematics (part: 20)
Category Algebra
Mathematics: Real Analysis
Mathematics: Complex Analysis
Analytic Topology
Number of Pages 380
Dimensions Width: 163mm
Height: 240mm
Spine: 27mm
Dewey Code 515.732
Weight 708g
Interest Age 19+ years
Reading Age 19+ years
Library of Congress Banach algebras, Banach spaces
NBS Text Science & Mathematics: Textbooks & Study Guides
ONIX Text College/higher education