Volume 4: Hilbert Spaces, 1st Edition

Hilbert Spaces, 1st Edition

Introduction.

5. Hilbert Spaces.

5.1 Pre-Hilbert Spaces.

5.1.1 General Results.

5.1.2 Examples.

5.1.3 Hilbert sums.

5.2 Orthogonal Projections of Hilbert space.

5.2.1 Projections onto Convex Sets.

5.2.2 Orthogonality.

5.2.3 Orthogonal Projections.

5.2.4 Mean Ergodic Theorems.

5.2.5 The Fréchet-Riesz Theorem.

5.3 Adjoint Operators.

5.3.1 General Results.

5.3.2 Supplementary Results.

5.3.3 Selfadjoint Operators.

5.3.4 Normal Operators.

5.4 Representations.

5.4.1 Cyclic Representation.

5.4.2 General Representations.

5.4.3 Example of Representations

5.5 Orthonormal Bases.

5.5.1 General Results.

5.5.2 Hilbert Dimension.

5.5.3 Standard Examples.

5.5.4 The Fourier-Plancherel Operator.

5.5.5 Operators and Orthonormal Bases.

5.5.6 Self-normal Compact Operators.

5.5.7 Examples of Real C*-algebras.

5.6 Hilbert right C*-Modules.

5.6.1 Some General Results.

5.6.2 Self-duality.

5.6.3 Von Neumann right W*-modules.

5.6.4 Examples.

5.6.5 KE.

5.6.6 Matrices over C*-algebras.

5.6.7 Type I W*-algebras.

Name Index. Subject Index. Symbol Index.