Amenable Banach Algebras: A Panorama

Preface
Introduction
Contents
0 Paradoxical Decompositions
	0.1 The Banach–Tarski Paradox
	0.2 Tarski\'s Theorem
1 Amenable, Locally Compact  Groups
	1.1 Invariant Means and Asymptotic Invariance Properties
	1.2 Hereditary Properties
	1.3 Uniformly Bounded Representations
	1.4 Leptin\'s Theorem
	1.5 Fixed Point Theorems
2 Amenable Banach Algebras
	2.1 Derivations from Group Algebras
	2.2 Virtual and Approximate Diagonals
	2.3 Hereditary and Splitting Properties
	2.4 A First Look at Hochschild Cohomology
3 Examples
	3.1 Measure Algebras
	3.2 Fourier and Fourier–Stieltjes Algebras
	3.3 Algebras of Approximable Operators
	3.4 (Non-)Amenability of mathcalB(E)
	3.5 An Amenable Radical Banach Algebra
4 Amenability-Like Properties
	4.1 Contractibility
	4.2 Weak Amenability
	4.3 Character Amenability
	4.4 Pseudo- and Approximate Amenability
	4.5 Biflatness and Biprojectivity
5 Dual Banach Algebras
	5.1 Connes-Amenability for Dual Banach Algebras
	5.2 The Case of the Measure Algebra
	5.3 Connes-Amenability without a Normal, Virtual Diagonal
	5.4 Daws\' Representation Theorem
	5.5 Connes-Amenability and Connes-Injectivity
6 Banach Homological Algebra
	6.1 Projectivity
	6.2 Resolutions and Ext-Groups
	6.3 Flatness and Injectivity
7 Operator Algebras on Hilbert  Spaces
	7.1 Amenable von Neumann Algebras
	7.2 Injective von Neumann Algebras
	7.3 Nuclear Cast-Algebras
	7.4 Semidiscrete von Neumann Algebras
	7.5 Normal, Virtual Diagonals
	7.6 Commutative Operator Algebras
	7.7 An Amenable Operator Algebra Not Similar to a Cast-Algebra
8 Operator Amenability
	8.1 Operator Amenable, Completely Contractive Banach Algebras
	8.2 Fourier Algebras
	8.3 Fourier–Stieltjes Algebras
A Banach Spaces
	A.1  Bases in Banach Spaces
	A.2  Approximation Properties
	A.3  The Radon–Nikodým Property
	A.4  Local Theory
B Banach Algebras
	B.1  Spectra and Gelfand Theory
	B.2  Banach Modules and Bounded Approximate Identities
	B.3  Multiplier Algebras
	B.4  Prime and Primitive ideals
	B.5  Structure of Semiprime and Semisimple Banach Algebras
C Cast- and von Neumann Algebras
	C.1  ast-Algebras and -Homomorphisms
	C.2  Cast-Algebras
	C.3  Positivity in Cast-Algebras and Their Duals
	C.4  ast-Representations of Cast-Algebras
	C.5  von Neumann Algebras and Wast-Algebras
	C.6  Multipliers of Cast-Algebras
	C.7  Projections in von Neumann Algebras
	C.8  Tensor Products of Cast- and von Neumann Algebras
	C.9  Weights on von Neumann algebras
D Abstract Harmonic Analysis
	D.1  Semitopological Semigroups and Locally Compact Groups
	D.2  The Group Algebra
	D.3  The Measure Algebra M(G)
	D.4  Other Banach Algebras Associated with Locally Compact Groups
E Operator Spaces
	E.1  Concrete and Abstract Operator Spaces
	E.2  Completely Bounded Maps
	E.3  Duality
	E.4  The Projective Tensor Product of Operator Spaces
	E.5  Completely Contractive Banach Algebras
F Fourier and Fourier–Stieltjes Algebras
	F.1  Representations of Locally Compact Groups
	F.2  The Fourier Algebra
	F.3  The Fourier–Stieltjes Algebra
	F.4  Cosets, Idempotents, and Piecewise Affine Maps
References
Index of Symbols
Index
Index of Names