Noncommutative Integration and Operator Theory (Progress in Mathematics, 349)

Preface
Acknowledgments
Contents
1 A Review of Relevant Operator Theory
	1.1 Bounded Hilbert Space Operators
	1.2 Topologies on the Space B( H)
	1.3 The Lattice of Projections
	1.4 Closed Linear Operators
	1.5 The Spectral Theorem
	1.6 Self-adjoint operators
	1.7 Polar Decomposition
	1.8 Quadratic Forms
	1.9 Algebras with an Involution
	1.10 C-Algebras
	1.11 Von Neumann Algebras
	1.12 Singular Functionals on von Neumann Algebras
	1.13 Direct Products of von Neumann Algebras
	1.14 Comparison of Projections
	1.15 Traces
2 Measurable Operators
	2.1 Affiliated Operators
	2.2 The Algebra of Measurable Operators
	2.3 The Algebra of τ-Measurable Operators
	2.4 The Algebra of τ-Compact Operators
	2.5 The Measure Topology in S( τ)
	2.6 Measure Topology and Order
	2.7 The Local Measure Topology
	2.8 Continuity of Operator Functions with Respect to the Measure Topology
	2.9 Trace Preserving -Homomorphisms
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3 Singular Value Functions
	3.1 The Right-Continuous Inverse of a Decreasing Function
	3.2 The Singular Value Function
	3.3 Extension of the Trace to S( τ) +
	3.4 The Space L1( τ)
	3.5 The Eigenvalue Function
	3.6 Properties of the Eigenvalue Function
	3.7 Some Auxiliary Results
	3.8 Submajorization for the Eigenvalue Function
	3.9 Submajorization for the Singular Value Function
	3.10 Contractions for the Couple ( L1( τ) ,L∞( τ) )
4 Symmetric Spaces of τ-Measurable Operators
	4.1 Normed M-Bimodules of τ-Measurable Operators
	4.2 The Dual of a Normed M-Bimodule
	4.3 The Köthe Dual of a Normed M-Bimodule
	4.4 Symmetric Spaces of τ-Measurable Operators
	4.5 The Köthe Dual of a Symmetric Space
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5 Strongly Symmetric Spaces of τ-Measurable Operators
	5.1 Strongly Symmetric Spaces and Their Köthe Duals
	5.2 Normal and Singular Functionals
	5.3 Order Continuity of the Norm
	5.4 Elements of Order Continuous Norm
	5.5 Elements of Absolutely Continuous Norm
	5.6 Further Characterizations of Order Continuity
	5.7 Sets of Uniformly Absolutely Continuous Norm
	5.8 Weakly Compact Subsets
	5.9 Embedding Copies of c0 and 1
6 Examples
	6.1 Construction of Symmetric Spaces
	6.2 Lp-spaces
	6.3 Lorentz Spaces
	6.4 Marcinkiewicz Spaces
	6.5 Orlicz Spaces
	6.6 p-Convexification
	6.7 Lorentz Lp,q-Spaces
	6.8 Sequence Spaces
7 Interpolation
	7.1 Basic Ideas
		7.1.1 Conditional Expectations
		7.1.2 Interpolation Functors
	7.2 Interpolation Spaces for the Couple (L1(τ),M)
	7.3 Principal Theorems on Noncommutative Interpolation
	7.4 The K-Functional
	7.5 Real Interpolation and the Noncommutative Marcinkiewicz Theorem
	7.6 Holmstedt Formula
	7.7 Operators of Weak Type and the Calderón Operator
	7.8 Noncommutative Marcinkiewicz Theorem for Sublinear Mappings
	7.9 The Boyd Interpolation Theorem
	7.10 Weak Type (p,p) and Strong Type (∞,∞) Interpolation
	7.11 Strong Type (1,1) and Weak Type (q,q) Interpolation, 1