Volume 200. Applications of Functional Analysis and Operator Theory

Preface. Acknowledgements. Contents. 1. Banach Spaces 1.1 Introduction 1.2 Vector Spaces 1.3 Normed Vector Spaces 1.4 Banach Spaces 1.5 Hilbert Space Problems 2. Lebesgue Integration and the Lp Spaces 2.1 Introduction 2.2 The Measure of a Set 2.3 Measurable Functions 2.4 Integration 2.5 The Lp Spaces 2.6 Applications Problems 3. Foundations of Linear Operator Theory 3.1 Introduction 3.2 The Basic Terminology of Operator Theory 3.3 Some Algebraic Properties of Linear Operators 3.4 Continuity and Boundedness 3.5 Some Fundamental Properties of Bounded Operators 3.6 First Results on the Solution of the Equation Lf=g 3.7 Introduction to Spectral Theory 3.8 Closed Operators and Differential Equations Problems 4. Introduction to Nonlinear Operators 4.1 Introduction 4.2 Preliminaries 4.3 The Contraction Mapping Principle 4.4 The Frechet Derivative 4.5 Newton's Method for Nonlinear Operators Problems 5. Compact Sets in Banach Spaces 5.1 Introduction 5.2 Definitions 5.3 Some Consequences of Compactness 5.4 Some Important Compact Sets of Functions Problems 6. The Adjoint Operator 6.1 Introduction 6.2 The Dual of a Banach