Linear Functional Analysis
by WWL Chen
This set of notes has been organized in such a way to create a single volume suitable for an introduction to some of the basic ideas in linear functional analysis. Chapters 1-2 were used in various forms and on many occasions between 1983 and 1990 by the author at Imperial College, University of London. Chapters 3-9 were added in Sydney in 2001.
To read the notes, click the chapters below for connection to the appropriate PDF files.
The material is available free to all individuals, on the understanding that it is not to be used for financial gain, and may be downloaded and/or photocopied, with or without permission from the author. However, the documents may not be kept on any information storage and retrieval system without permission from the author, unless such system is not accessible to any individuals other than its owners.
Chapter 1: INTRODUCTION TO METRIC SPACES
Chapter 2: CONNECTEDNESS, COMPLETENESS AND COMPACTNESS
Chapter 3: NORMED VECTOR SPACES
Chapter 4: INNER PRODUCT SPACES
Chapter 5: ORTHOGONAL EXPANSIONS
Chapter 6: LINEAR FUNCTIONALS
Chapter 7: INTRODUCTION TO LINEAR TRANSFORMATIONS
Chapter 8: LINEAR TRANSFORMATIONS ON HILBERT SPACES
Chapter 9: SPECTRUM OF A LINEAR OPERATOR