Lectures on amenability

• Main Author: Runde, Volker
• Format: eBook Book
• Language: English
• Published: Berlin, Heidelberg Springer-Verlag 2002; Springer Berlin / Heidelberg; Springer Berlin Heidelberg; Springer
• Edition: 1
• Series: Lecture Notes in Mathematics
• Subjects: Abstract Harmonic Analysis; Algebra; Banach alegebras; Banach algebras; Category Theory, Homological Algebra; Functional Analysis; Global analysis; Global Analysis and Analysis on Manifolds; Harmonic analysis; Mathematics; Mathematics and Statistics; Measure alegbras; Measure theory; Tranformations (Mathematics)
• ISBN: 9783540428527; 3540428526; 3662185431; 9783662185438
• ISSN: 0075-8434; 1617-9692
• DOI: 10.1007/b82937

The notion of amenability has its origins in the beginnings of modern measure theory: Does a finitely additive set function exist which is invariant under a certain group action? Since the 1940s, amenability has become an important concept in abstract harmonic analysis (or rather, more generally, in...

Table of Contents:

• A.3 Regular representations on Lp(G) and associated algebras -- A.4 Notes and comments -- B.1 The algebraic tensor product -- B.2 Banach space tensor products -- B.2.1 The injective tensor product -- B.2.2 The projective tensor product -- B.3 The Hilbert space tensor product -- B.4 Notes and comments -- C.1 Approximation properties -- C.2 The Radon‒Nikodým property -- C.3 Local theory of Banach spaces -- C.4 Notes and comments -- D.1 Abstract and concrete operator spaces -- D.2 Completely bounded maps -- D.3 Tensor products of operator spaces -- D.4 Operator Banach algebras -- D.5 Notes and comments -- List of symbols -- References -- Index
• Intro -- Title -- Preface -- 0.1 The Banach-Tarski paradox -- 0.2 Tarski's theorem -- 0.3 Notes and comments -- 1.1 Invariant means on locally compact groups -- 1.2 Hereditary properties -- 1.3 Day's fixed point theorem -- 1.4 Representations on Hilbert space -- 1.5 Notes and comments -- Følner type conditions -- Weak containment of unitary representations -- 2.1 Johnson's theorem -- 2.2 Virtual and approximate diagonals -- 2.3 Hereditary properties -- 2.4 Hochschild cohomology -- 2.5 Notes and comments -- 3.1 Banach algebras of compact operators -- 3.2 A commutative, radical, amenable Banach algebra -- 3.3 Notes and comments -- 4.1 Super-amenability -- 4.2 Weak amenability -- 4.3 Biprojectivity and biflatness -- 4.4 Connes-amenability -- 4.5 Notes and comments -- 5.1 Projectivity -- 5.2 Resolutions and Ext-groups -- 5.3 Flatness and injectivity -- 5.4 Notes and comments -- Forbidden values for homological dimensions -- Additivity formulae for homological dimensions -- 6.1 Amenable W*-algebras -- 6.2 Injective W*-algebras -- 6.3 Tensor products of C*- and W*-algebras -- 6.4 Semidiscrete W*-algebras -- 6.5 Normal, virtual diagonals -- 6.6 Notes and comments -- 7.1 Bounded approximate identities for Fourier algebras -- 7.2 (Non-)amenability of Fourier algebras -- 7.3 Operator amenable operator Banach algebras -- 7.4 Operator amenability of Fourier algebras -- 7.5 Operator amenability of C*-algebras -- 7.6 Notes and comments -- 8.1 Infnite-dimensional differential geometry -- 8.2 Spaces of homomorphisms -- 8.3 Notes and comments -- Amenable, locally compact groups -- Amenable Banach algebras -- Examples of amenable Banach algebras -- Amenability-like properties -- Banach homology -- C*- and W*-algebras -- Operator amenability -- Geometry of spaces of homomorphisms -- A.1 Convolution of measures and functions -- A.2 Invariant subspaces of L∞(G)
• Paradoxical decompositions -- Amenable, locally comact groups -- Amenable Banach algebras -- Exemples of amenable Banach algebras -- Amenability-like properties -- Banach homology -- C* and W*-algebras -- Operator amenability -- Geometry of spaces of homomorphisms -- Open problems: Abstract harmonic analysis -- Tensor products -- Banach space properties -- Operator spaces -- List of symbols -- References -- Index.