Contents
PREFACE TO THE REVISED EDITION xv
FROM THE PREFACE TO THE FIRST EDITION xix
Chapter 1. BASIC NOTIONS 1
§1.1. A problem from differential equations 1
§1.2. An examination of the results 6
§1.3. Examples of Banach spaces 9
§1.4. Fourier series 17
§1.5. Problems 24
Chapter 2. DUALITY 29
§2.1. The Riesz representation theorem 29
§2.2. The Hahn-Banach theorem 33
§2.3. Consequences of the Hahn-Banach theorem 36
§2.4. Examples of dual spaces 39
§2.5. Problems 51
Chapter 3. LINEAR OPERATORS 55
§3.1. Basic properties 55
§3.2. The adjoint operator 57
§3.3. Annihilators 59
§3.4. The inverse operator 60
§3.5. Operators with closed ranges 66
§3.6. The uniform boundedness principle 71
ix
Previous Page Next Page