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Introduction to Banach Spaces and Algebras (Paperback)
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Introduction to Banach Spaces and Algebras (Paperback)
Series: Oxford Graduate Texts in Mathematics, 20
Expected to ship within 12 - 19 working days
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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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