Lectures on Amenability

0 Paradoxical decompositions0.1 The Banach-Tarski paradox0.2 Tarski's theorem0.3 Notes and comments1 Amenable, locally comact groups1.1 Invariant means on locally compact groups1.2 Hereditary properties1.3 Day's fixed point theorem1.4 Representations on Hilbert space1.5 Notes and comments2 Amenable Banach algebras2.1 Johnson's theorem2.2 Virtual and approximate diagonals2.3 Hereditary properties2.4 Hochschild cohomology2.5 Notes and comments3 Exemples of amenable Banach algebras 3.1 Banach algebras of compact operators3.2 A commutative, radical, amenable Banach algebra3.3 Notes and comments4 Amenability-like properties4.1 Super-amenability4.2 Weak amenability4.3 Biprojectivity and biflatness4.4 Connes-amenability4.5 Notes and comments5 Banach homology5.1 Projectivity5.2 Resolutions and Ext-groups5.4 Flatness and injectivity5.4 Notes and Comments6 C* and W*-algebras6.1 Amenable W*-algebras6.2 Injective W*-algebras6.3 Tensor products of C*- and W*-algebras6.4 Semidiscrete W*-algebras6.5 Normal, virtual diagonals6.6 Notes and comments7.1 Bounded approximate identities for Fourier algebras7.2 (Non-)amenability of Fourier7.3 Operator amenable operator Banach algebras7.4 Operator amenability of Fourier algebras7.5 Operator amenability of C*-algebras7.6 Notes and comments8 Geometry of spaces of homomorphisms8.1 Infinite-dimensional differential geometry8.2 Spaces of homomorphisms8.3 Notes and CommentsOpen problemsA Abstract harmonic analysisA.1 Convolution of measures and functionsA.2 Invariant subspaces of L(infinity symbol)(G)A.3 Regular representations on Lp(G)A.4 Notes and commentsB.1 The algebraic tensor productsB.2 Banach space tensor productsB.2.1 The injective tensor product B.2.2 The projective tensor productB.3 The Hilbert space tensor productB.4 Notes and commentsC Banach space propertiesC.1 Approximation propertiesC.2 The Radon-Nikokym propertyC.3 Local theory of Banach spacesC.4 Notes and commentsD Operator spacesD.1 Abstract and concrete operator spacesD.2