Introduction to the Analysis of Normed Linear Spaces

J. R. Giles

doi:10.1017/CBO9781139168465

This text is a basic course in functional analysis for senior undergraduate and beginning postgraduate students. It aims at providing some insight into basic abstract analysis which is now the contextual language of much modern mathematics. Although it is assumed that the student will have familiarity with elementary real and complex analysis and linear algebra and have studied a course in the analysis of metric spaces, a knowledge of integration theory or general topology is not required. The theme of this text concerns structural properties of normed linear spaces in general, especially associated with dual spaces and continuous linear operators on normed linear spaces. But the implications of the general theory are illustrated 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 …’.

Source: Australian Mathematical Society Gazette

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Introduction to the Analysis of Normed Linear Spaces

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Contents

Frontmatter
pp i-vi

Contents
pp vii-x

Preface
pp xi-xiv

Chapter I - NORMED LINEAR SPACE STRUCTURE AND EXAMPLES
pp 1-66

Chapter II - SPACES OF CONTINUOUS LINEAR MAPPINGS
pp 67-112

Chapter III - THE EXISTENCE OF CONTINUOUS LINEAR FUNCTIONALS
pp 113-138

Chapter IV - THE FUNDAMENTAL MAPPING THEOREMS FOR BANACH SPACES
pp 139-170

Chapter V - TYPES OF CONTINUOUS LINEAR MAPPINGS
pp 171-216

Chapter VI - SPECTRAL THEORY
pp 217-251

Appendix
pp 252-257

Historical notes
pp 258-268

List of symbols
pp 269-270

List of spaces
pp 271-271

Index
pp 272-280

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