John R Ringrose

Indeholder "Preface", "Contents of Volume I", "Chapter 6. Comparison Theory of Projection", " 6.1 Polar decomposition and equivalence", " 6.2 Ordering", " 6.3 Finite and infinite projections", " 6.4 Abelian projections", " 6.5 Type decomposition", " 6.6 Type I algebras", " 6.7 Examples", " 6.8 Ideals", " 6.9 Exercises", "Chapter 7. Normal States and Unitary Equivalence of von Neumann Algebras", " 7.1 Completely additive states", " 7.2 Vector states and unitary implementation", " 7.3 A second show more approach to normal states", " 7.4 The predual", " 7.5 Normal weights on von Neumann algebras", " 7.6 Exercises", "Chapter 8. The Trace", " 8.1 Traces", " 8.2 The trace in finite algebras", " 8.3 The Dixmier approximation theorem", " 8.4 The dimension function", " 8.5 Tracial weights on factors", " 8.6 Further examples of factors", " An operator-theoretic construction", " Measure-theoretic examples", " 8.7. Exercises", "Chapter 9. Algebra and Commutant", " 9.1. The type of the commutant", " 9.2 Modular theory", " A first approach to modular theory", " Tomita's theorem - a second approach", " A further extension of modular theory", " 9.3. Unitary equivalence of type I algebras", " 9.4. Abelian von Neumann algebras", " 9.5. Spectral multiplicity", " 9.6. Exercises", "Chapter 10. Special Representation of C*-Algebras", " 10.1. The universal representation", " 10.2. Irreducible representations", " 10.3. Disjoint representations", " 10.4. Examples", " Abelian C*-algebras", " Compact operators", " B(H) and the Calkin algebra", " Uniformly matricial algebras", " 10.5. Exercises", "Chapter 11. Tensor Products", " 11.1. Tensor products of represented C*-algebras", " 11.2. Tensor products of von Neumann algebras", " Elementary properties", " The commutation theorem", " The type of tensor products", " Tensor products of unbounded operators", " 11.3. Tensor products of abstract C*-algebras", " The spatial tensor product", " C*-norms on A . B", " Nuclear C*-algebras", " 11.4 Infinite tensor products of C*-algebras", " 11.5 Exercises", "Chapter 12. Approximation by Matrix Algebras", " 12.1 Isomorphism of uniformly matricial algebras", " 12.2 The finite matricial factor", " 12.3 States and representations of matricial C*-algebras", " 12.4 Exercises", "Chapter 13. Crossed Products", " 13.1 Discrete crossed products", " 13.2 Continuous crossed products", " 13.3 Crossed products by modular automorphism groups", " 13.4 Exercises", "Chapter 14. Direct Integrals and Decompositions", " 14.1 Direct integrals", " 14.2 Decompositions relative to abelian algebras", " 14.3 Appendix - Borel mappings and analytic sets", " 14.4 Exercises", "Bibliography", "Index of Notation", "Index".

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Indeholder "Preface", "Contents of Volume II", "Chapter 1. Linear Spaces", " 1.1 Algebraic results", " 1.2 Linear topological Spaces", " 1.3 Weak topologies", " 1.4 Extreme points", " 1.5 Normed spaces", " 1.6 Linear functionals on normed spaces", " 1.7 Some examples of Banach spaces", " 1.8 Linear operators acting on Banach spaces", " 1.9 Exercises", "Chapter 2. Basics of Hilbert Space and Linear Operators", " 2.1 Inner products on linear spaces", " 2.2 Orthogonality", " 2.3 The weak show more topology", " 2.4 Linear operators", " General theory", " Classes of operators", " 2.5 The lattice of projections", " 2.6 Constructions with Hilbert spaces", " Subspaces", " Direct sums", " Tensor products and the Hilbert-Schmidt class", " Matrix representations", " 2.7 Unbounded linear operators", " 2.8 Exercises", "Chapter 3. Banach Algebras", " 3.1 Basics", " 3.2 The spectrum", " The Banach algebra L1(R) and Fourier analysis", " 3.3 The Holomorphic Function Calculus", " Holomorphic functions", " The holomorphic function calculus", " 3.4 The Banach algebra C(X)", " 3.5 Exercises", "Chapter 4. Elementary C*-Algebra Theory", " 4.1 Basics", " 4.2 Order structure", " 4.3 Positive linear functionals", " 4.4 Abelian algebras", " 4.5 States and representations", " 4.6 Exercises", "Chapter 5. Elementary von Neumann Algebra Theory", " 5.1 The weak- and strong-operator topologies", " 5.2 Spectral theory for bounded operators", " 5.3 Two fundamental approximation theorems", " 5.4 Irreducible algebras - an application", " 5.5 Projection techniques and constructs", " Central carriers", " Some constructions", " Cyclicity, separation, and countable decomposability", " 5.6 Unbounded operators and abelian von Neumann Algebras", " 5.7 Exercises", "Bibliography", "Index of Notation", "Index".

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