Banach Lattices: Universitext

1 Riesz Spaces.- 1.1 Basic Properties of Riesz Spaces and Banach Lattices.- 1.2 Sublattices, Ideals, and Bands.- 1.3 Regular Operators and Order Bounded Functionals.- 1.4 Duality of Riesz Spaces, the Nakano Theory.- 1.5 Extensions of Positive Operators.- 2 Classical Banach Lattices.- 2.1 C(K)-Spaces and M-Spaces.- 2.2 Complex Riesz Spaces.- 2.3 Disjoint Sequences and Approximately Order Bounded Sets.- 2.4 Order Continuity of the Norm, KB-Spaces and the Fatou Property.- 2.5 Weak Compactness.- 2.6 Banach Function Spaces.- 2.7 Lp-Spaces and Related Results.- 2.8 Cone p-Absolutely Summing Operators and p-Subadditive Norms.- 3 Operators on Riesz Spaces and Banach Lattices.- 3.1 Disjointness Preserving Operators and Orthomorphisms on Riesz Spaces.- 3.2 Operators on L-and M-Spaces.- 3.3 Kernel Operators.- 3.4 Order Weakly Compact Operators.- 3.5 Weakly Compact Operators.- 3.6 Approximately Order Bounded Operators.- 3.7 Compact Operators and Dunford-Pettis Operators.- 3.8 Tensor Products of Banach Lattices.- 3.9 Vector Measures and Vectorial Integration.- 4 Spectral Theory of Positive Operators.- 4.1 Spectral Properties of Positive Linear Operators.- 4.2 Irreducible Operators.- 4.3 Measures of Non-Compactness.- 4.4 Local Spectral Theory for Positive Operators.- 4.5 Order Spectrum of Regular Operators.- 4.6 Disjointness Preserving Operators and the Zero-Two Law.- 5 Structures in Banach Lattices.- 5.1 Banach Space Properties of Banach Lattices.- 5.2 Banach Lattices with Subspaces Isomorphic to C(?), C(0,l), and L1(0,1).- 5.3 Grothendieck Spaces.- 5.4 Radon-Nikodym Property in Banach Lattices.- References.