Banach Lattices and Positive Operators

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