TY  - BOOK
AU  - Rynne,Bryan P.
AU  - Youngson,Martin A.
TI  - Linear functional analysis
T2  - Springer undergraduate mathematics series
SN  - 1852332573
AV  - QA320 .R96 2000
PY  - 2000///]
CY  - London, New York
PB  - Springer
KW  - Functional analysis
N1  - 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
ER  -