Author | Zaanen, Adriaan C. author |
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Title | Introduction to Operator Theory in Riesz Spaces [electronic resource] / by Adriaan C. Zaanen |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1997 |
Connect to | http://dx.doi.org/10.1007/978-3-642-60637-3 |
Descript | XI, 312p. online resource |
1 Lattices and Boolean Algebras -- 1 Partially Ordered Sets -- 2 Lattices -- 3 Boolean Algebras -- 2 Riesz Spaces -- 4 Riesz Spaces -- 5 Equalities and Inequalities -- 6 Distributive Laws, the Birkhoff Inequalities and the Riesz Decomposition Property -- 3 Ideals, Bands and Disjointness -- 7 Ideals and Bands -- 8 Disjointness -- 4 Archimedean Spaces and Convergence -- 9 Archimedean Riesz spaces -- 10 Order Convergence and Uniform Convergence -- 5 Projections and Dedekind Completeness -- 11 Projection Bands -- 12 Dedekind Completeness -- 6 Complex Riesz Spaces -- 13 Complex Riesz spaces -- 7 Normed Riesz Spaces and Banach Lattices -- 14 Normed Spaces and Banach Spaces -- 15 Normed Riesz Spaces and Banach Lattices -- 8 The Riesz-Fischer Property and Order Continuous Norms -- 16 The Riesz-Fischer Property -- 17 Order Continuous Norms -- 9 Linear Operators -- 18 Linear Operators in Normed Spaces and in Riesz Spaces -- 19 Riesz Homomorphisms and Quotient Spaces -- 10 Order Bounded Operators -- 20 Order Bounded Operators -- 11 Order Continuous Operators -- 21 Order Continuous Operators -- 22 The Band of Order Continuous Operators -- 12 Carriers of Operators -- 23 Order Denseness -- 24 The Carrier of an Operator -- 13 Order Duals and Adjoint Operators -- 25 The Order Dual of a Riesz Space -- 26 Adjoint Operators -- 14 Signed Measures and the Radon-Nikodym Theorem -- 27 The Space of Signed Measures -- 28 The Radon-Nikodym Theorem -- 15 Linear Functionals on Spaces of Measurable Functions -- 29 Linear Functionals on Spaces of Measurable Functions -- 16 Embedding into the Bidual -- 30 Annihilators and Inverse Annihilators -- 31 Embedding into the Order Bidual -- 17 Freudenthalโs Spectral Theorem -- 32 Projection Bands and Components -- 33 Freudenthalโs Spectral Theorem -- 18 Functional Calculas and Multiplication -- 34 Functional Calculus -- 35 Multiplication -- 19 Complex Operators -- 36 Complex Operators -- 37 Synnatschkeโs Theorem -- 20 Results with the Hahn-Banach Theorem -- 38 The Hahn-Banach Theorem in Normed Vector Spaces -- 39 The Hahn-Banach Theorem in Normed Riesz Spaces -- 21 Spectrum, Resolvent Set and the Krein-Rutman Theorem -- 40 Spectrum and Resolvent Set -- 41 The Krein-Rutman Theorem -- 22 Spectral Theory of Positive Operators -- 42 Irreducible Operators -- 43 The Spectrum of a Compact Irreducible Operator -- 44 The Peripheral Spectrum of a Positive Operator