Linear functional analysis / Bryan P. Rynne and Martin A. Youngson

Includes bibliographical references (pages 267-268) and index

1. Preliminaries -- 1.1. Linear Algebra -- 1.2. Metric Spaces -- 1.3. Lebesgue Integration -- 2. Normed Spaces -- 2.1. Examples of Normed Spaces -- 2.2. Finite-dimensional Normed Spaces -- 2.3. Banach Spaces -- 3. Inner Product Spaces, Hilbert Spaces -- 3.1. Inner Products -- 3.2. Orthogonality -- 3.3. Orthogonal Complements -- 3.4. Orthonormal Bases in Infinite Dimensions -- 3.5. Fourier Series -- 4. Linear Operators -- 4.1. Continuous Linear Transformations -- 4.2. The Norm of a Bounded Linear Operator -- 4.3. The Space B(X,Y) and Dual Spaces -- 4.4. Inverses of Operators -- 5. Linear Operators on Hilbert Spaces -- 5.1. The Adjoint of an Operator -- 5.2. Normal, Self-adjoint and Unitary Operators -- 5.3. The Spectrum of an Operator -- 5.4. Positive Operators and Projections -- 6. Compact Operators -- 6.1. Compact Operators -- 6.2. Spectral Theory of Compact Operators -- 6.3. Self-adjoint Compact Operators -- 7. Integral and Differential Equations -- 7.1. Fredholm Integral Equations -- 7.2. Volterra Integral Equations -- 7.3. Differential Equations -- 7.4. Eigenvalue Problems and Green's Functions -- 8. Solutions to Exercises