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Introduction to the Analysis of Normed Linear Spaces : Australian Mathematical Society Lecture Series, 13 - J. R. Giles

Introduction to the Analysis of Normed Linear Spaces

Australian Mathematical Society Lecture Series, 13

Paperback

Published: 15th April 2000
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This text is ideal for a basic course in functional analysis for senior undergraduate and beginning postgraduate students. John Giles provides insight into basic abstract analysis, which is now the contextual language of much modern mathematics. Although it is assumed that the student has familiarity with elementary real and complex analysis, linear algebra, and the analysis of metric spaces, the book does not assume a knowledge of integration theory or general topology. Its central theme concerns structural properties of normed linear spaces in general, especially associated with dual spaces and continuous linear operators on normed linear spaces. Giles illustrates the general theory with a great variety of example spaces.

'... the text is up-to-date and detailed in exposition, and is large enough in material covered for different courses to be constructed from it ...'. Australian Mathematical Society Gazette

Basic properties of normed linear spaces
Classes of example spaces
Orthonormal sets in inner product spaces
Norming mappings and forming duals and operator algebras
The shape of the dual
The Hahn-Banach theorem
The natural embedding and reflexivity
Subreflexivity
Baire category theory for metric spaces
The open mapping and closed graph theorems
The uniform boundedness theorem
Conjugate mappings
Adjoint operators on Hilbert space
Projection operators
Compact operators
The spectrum
The spectrum of a continuous linear operator
The spectrum of a compact operator
The spectral theorem for compact normal operators on Hilbert space
The spectral theorem for compact operators on Hilbert space
Appendices
Zorn's lemma
Numerical equivalence
Hamel basis
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521653756
ISBN-10: 0521653754
Series: Australian Mathematical Society Lecture Series, 13
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 180
Published: 15th April 2000
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 22.86 x 15.24  x 1.91
Weight (kg): 0.41