Skip to content
You are not logged in |Login  
     
Limit search to available items
Record:   Prev Next
Resources
More Information
Bestseller
BestsellerE-book
Author Allan, Graham R., 1936-2007.

Title Introduction to Banach spaces and algebras / Graham Allan ; prepared for publication by H. Garth Dales.

Publication Info. Oxford : Oxford University Press, 2011.

Item Status

Description 1 online resource (vii, 371 pages).
Physical Medium polychrome
Description text file
Series Oxford graduate texts in mathematics ; 20
Oxford graduate texts in mathematics ; 20.
Bibliography Includes bibliographical references and index.
Summary 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.
Contents pt. I. Introduction to Banach spaces. 1. Preliminaries -- 2. Elements of normed spaces -- 3. Banach spaces -- pt. II. Introduction to Banach algebras. 4. Banach algebras -- 5. Representation theory -- 6. Algebras with an involution -- 7. The Borel functional calculus -- pt. III. Several complex variables and Banach algebras. 8. Introduction to several complex variables -- 9. The holomorphic functional calculus in several variables.
Local Note eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America
Subject Banach spaces.
Banach spaces.
Banach algebras.
Banach algebras.
Genre/Form Electronic books.
Added Author Dales, H. G. (Harold G.), 1944-
Other Form: Print version: Allan, Graham R., -2007. Introduction to Banach spaces and algebras 9780199206544 (DLC) 2011292228 (OCoLC)691395481
ISBN 9780191548543 (electronic book)
0191548545 (electronic book)
9780199206544
9780199206537
0199206538
0199206546