Banach Lattices and Positive Operators

Inhaltsverzeichnis

• I. Positive Matrices.
• § 1. Linear Operators on ? n.
• § 2. Positive Matrices.
• § 3. Mean Ergodicity.
• § 4. Stochastic Matrices.
• § 5. Doubly Stochastic Matrices.
• § 6. Irreducible Positive Matrices.
• § 7. Primitive Matrices.
• § 8. Invariant Ideals.
• § 9. Markov Chains.
• § 10. Bounds for Eigenvalues.
• Notes.
• Exercises.
• II. Banach Lattices.
• § 1. Vector Lattices over the Real Field.
• § 2. Ideals, Bands, and Projections.
• § 3. Maximal and Minimal Ideals. Vector Lattices of Finite Dimension.
• § 4. Duality of Vector Lattices.
• § 5. Normed Vector Lattices.
• § 6. Quasi-Interior Positive Elements.
• § 7. Abstract M-Spaces.
• § 8. Abstract L-Spaces.
• § 9. Duality of AM- and AL-Spaces. The Dunford-Pettis Property.
• § 10. Weak Convergence of Measures.
• § 11. Complexification.
• III. Ideal and Operator Theory.
• § 1. The Lattice of Closed Ideals.
• § 2. Prime Ideals.
• § 3. Valuations.
• § 4. Compact Spaces of Valuations.
• § 5. Representation by Continuous Functions.
• § 6. The Stone Approximation Theorem.
• § 7. Mean Ergodic Semi-Groups of Operators.
• § 8. Operator Invariant Ideals.
• § 9. Homomorphisms of Vector Lattices.
• § 10. Irreducible Groups of Positive Operators. The Halmos-von Neumann Theorem.
• § 11. Positive Projections.
• IV. Lattices of Operators.
• § 1. The Modulus of a Linear Operator.
• § 2. Preliminaries on Tensor Products. New Characterization of AM- and AL-Spaces.
• § 3. Cone Absolutely Summing and Majorizing Maps.
• § 4. Banach Lattices of Operators.
• § 5. Integral Linear Mappings.
• § 6. Hilbert-Schmidt Operators and Hilbert Lattices.
• § 7. Tensor Products of Banach Lattices.
• § 8. Banach Lattices of Compact Maps. Examples.
• § 9. Operators Defined by Measurable Kernels.
• § 10. Compactness of Kernel Operators.
• V. Applications.
• § 1. An Imbedding Procedure.
• § 2. Approximation of Lattice Homomorphisms (Korovkin Theory).
• § 3. Banach Lattices and Cyclic Banach Spaces.
• § 4. The Peripheral Spectrum of Positive Operators.
• § 5. The Peripheral point Spectrum of Irreducible Positive Operators.
• § 6. Topological Nilpotency of Irreducible Positive Operators.
• § 7. Application to Non-Positive Operators.
• § 8. Mean Ergodicity of Order Contractive Semi-Groups. The Little Riesz Theorem.
• Index of Symbols.