Placeholder text

Go to cart

Introduction to Banach Spaces and Algrebras

By Allan, Graham R.

Introduction to Banach Spaces and Algrebras

By Allan, Graham R.

- Default Title
Description
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.
Product details
Edition:
1
Number of Pages:
380
Release Date:
2010-12-30
Publication Date:
2010-11-04
Publisher:
OUP Oxford
Languages:
Original: English
ISBN10:
0199206538
ISBN13:
9780199206537
GPSR Manufacturer Reference:
[email protected]
Weight:
734 g
Height:
161 cm
Width:
240 cm
Thickness:
25 cm
Buy on Amazon
Currently sold out