目录 Preface Introduction List of Symbols Chapter 1 Metric Spaces 1.1 Preliminaries 1.2 Definitions and Examples 1.3 Convergence of Sequences in Metric Spaces 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 Banach Fixed Point Theorem Chapter 2 Normed Linear Spaces.Banach Spaces 2.1 Review of Linear Spaces 2.2 Norms in Linear Spaces 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 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 Bounded Linear Operators and Functionals 4.2 Spaces of Bounded Linear Operators and Dual Spaces 4.3 Banach-Steinhaus Theorem 4.4 Inverses of Operators. Banach's Theorem 4.5 Hahn-Banach Theorem 4.6 Strong and Weak Convergence Chapter 5 Linear Operators on Hilbert Spaces 5.1 Adjoint Operators. Lax-Milgram Theorem 5.2 Spectral Theorem for Self-adjoint Compact Operators Chapter 6 Differential Calculus in Normed Linear Spaces 6.1 Gateaux and Frechet Derivatives 6.2 Taylor's Formla, Implicit and Inverse Function Theorems Bibliography Index
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