Preface List of Symbols Chapter 1 Metric Spaces 1.1 Preliminaries 1.2 Definitions and Examples 1.3 Convergence in a Metric Space 1.4 Sets in a Metric Space 1.5 Complete Metric Spaces 1.6 Continuous Mappings on Metric Spaces 1.7 Compact Metric Spaces 1.8 The Contraction Mapping Principle Chapter 2 Normed Linear Spaces. Banach Spaces 2.1 Review of Linear Spaces 2.2 Norm in a Linear Space 2.3 Examples of Normed Linear Spaces 2.4 Finite Dimensional Normed Linear Spaces 2.5 Linear Subspaces of Normed Linear Spaces 2.6 Quotient Spaces 2.7 The Weierstrass Approximation Theorem Chapter 3 Inner Product Spaces. Hilbert Spaces 3.1 Inner Products 3.2 Orthogonality 3.3 Orthonormal Systems 3.4 Fourier Series Chapter 4 Linear Operators. Fundamental Theorems 4.1 Continuous Linear Operators and Functionals 4.2 Spaces of Bounded Linear Operators and Dual Spaces 4.3 The Banach-Steinhaus Theorem 4.4 Inverses of Operators. The Banach Theorem 4.5 The Hahn-Banach Theorem 4.6 Strong and Weak Convergence Chapter 5 Linear Operators on Hilbert Spaces 5.1 Adjoint Operators. The Lax-Milgram Theorem 5.2 Spectral Theorem for Self-adjoint Compact Operators Bibliography Index
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