Fundamentals of the Theory of Operator Algebras. V2
Advanced Theory
- 1st Edition, Volume 100II - June 10, 1986
- Latest edition
- Editors: Richard V. Kadison, John R. Ringrose
- Language: English
Preface
Contents of Volume I
Chapter 1 Linear Spaces
Chapter 2 Basics of Hilbert Space and Linear Operators
Chapter 3 Banach Algebras
Chapter 4 Elementary C*-Algebra Theory
Chapter 5 Elementary von Neumann Algebra Theory
Chapter 6: Comparison Theory of Projections
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 Example
6.7.1 Lemma
6.7.2 Theorem
6.7.3 Remark
6.7.4 Proposition
6.7.5 Theorem
6.7.6 Example
6.7.7 Example
6.7.8 Theorem
6.7.9 Remark
6.7.10 Theorem
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 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
8.7 Exercises
Chapter 9: Algebra and Commutant
9.1 The type of the commutant
9.2 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 Representations of C*-Algebras
10.1 The universal representation
10.2 Irreducible representations
10.3 Disjoint representations
10.4 Examples
10.5 Exercises
Chapter 11: Tensor Products
11.1 Tensor products of represented C*-algebras
11.2 Tensor products of von Neumann algebras
11.3 Tensor products of abstract 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
Algebras and related matters
Direct sums and integrals
Equivalences and orderings
Inner products and norms
Linear operators
Linear spaces
Linear topological spaces, Banach spaces, Hilbert spaces
Modular theory
Multiplicity theory
Sets and mappings
Special Banach spaces
States and weights
Tensor products and crossed products
Index
- Edition: 1
- Latest edition
- Volume: 100II
- Published: June 10, 1986
- Language: English
RK
Richard V. Kadison
Affiliations and expertise
Department of Mathematics, University of Pennsylvania,Philadelphia, PennsylvaniaJR
John R. Ringrose
Affiliations and expertise
School of Marhematics, University of Newcastle,
Newcastle upon Tyne, EnglandRead Fundamentals of the Theory of Operator Algebras. V2 on ScienceDirect