Inner Amenable Locally Compact Groups

DOI10.2307/2001664zbMath0718.43002OpenAlexW4230667909MaRDI QIDQ5749799

Anthony To-Ming Lau, Alan L. T. Paterson

Publication date: 1991

Full work available at URL: https://doi.org/10.2307/2001664

zbMATH Keywords

von Neumann algebralocally compact groupunitary operatorsRadon measureproperty (P)inner amenabilityG-invariant meanweak \({}^ *\)- closed convex hull

Mathematics Subject Classification ID

General theory of von Neumann algebras (46L10) (C^*)-algebras and (W^*)-algebras in relation to group representations (22D25) Means on groups, semigroups, etc.; amenable groups (43A07)

Related Items (20)

On exotic group C*-algebras ⋮ Similarity degree of Fourier algebras ⋮ On inner amenability of Clifford semigroups ⋮ Completely positive completion of partial matrices whose entries are completely bounded maps ⋮ Amenability and covariant injectivity of locally compact quantum groups ⋮ Amenable locally compact semigroups and a fixed point property ⋮ Amenable and inner amenable actions and approximation properties for crossed products by locally compact groups ⋮ On the operator homology of the Fourier algebra and its \(cb\)-multiplier completion ⋮ \(\Gamma \)-amenability of locally compact groups ⋮ Inner amenability and approximation properties of locally compact quantum groups ⋮ Strongly amenable semigroups and nonlinear fixed point properties ⋮ Inner invariant means and conjugation operators ⋮ Property $(T)$ for locally compact groups and $C^*$-algebras ⋮ Amenability for twisted covariance algebras and group \(C^*\)-algebras ⋮ A generalization of amenability and inner amenability of groups ⋮ Amenability of Banach and C$^*$-algebras generated by unitary representations ⋮ Amenability properties of unitary co-representations of locally compact quantum groups ⋮ Kirchberg's factorization property for locally compact groups ⋮ A weak expectation property for operator modules, injectivity and amenable actions ⋮ Amenability and exactness for dynamical systems and their 𝐶*-algebras

Cites Work

• Fixed-point theorems for compact convex sets
• The existence of inner invariant means on \(L^{\infty}(G)\)
• Classification of injective factors. Cases \(\mathrm{II}_1\), \(\mathrm{II}_\infty\), \(\mathrm{III}_\lambda\), \(\lambda\neq 1\)
• Fixed points and amenability: a counterexample
• Unbounded conjugacy classes in Lie groups and location of central measures
• Amenable actions of locally compact groups
• Derivations of simple \(C^ *\)-algebras. III
• Translation-Invariant Linear Forms on L p (G)
• Conjugation-invariant means
• Operator Theoretic Characterizations of [ IN -Groups and Inner Amenability]
• Dual Spaces of Groups with Precompact Conjugacy Classes
• Property Γ and Inner Amenability
• On the von Neumann Algebra of an Ergodic Group Action
• Inner Amenability and Conjugation Operators
• Folner's Conditions for Amenable Semi-Groups.
• Amenable Groups and Groups with the Fixed Point Property
• Compactness conditions in topological groups.
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