The Exact Cardinality of the Set of Topological Left Invariant Means on an Amenable Locally Compact Group

DOI10.2307/2045771zbMath0595.43003OpenAlexW4234252833MaRDI QIDQ3726721

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

Publication date: 1986

Full work available at URL: https://doi.org/10.2307/2045771

zbMATH Keywords

invariant subsetsinvariant meansamenable locally compact group

Mathematics Subject Classification ID

Cardinality properties (cardinal functions and inequalities, discrete subsets) (54A25) General properties and structure of locally compact groups (22D05) Means on groups, semigroups, etc.; amenable groups (43A07) Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions (43A60)

Related Items (16)

Multiple disjointness and invariant measures on minimal distal flows ⋮ One-sided ideals and right cancellation in the second dual of the group algebra and similar algebras ⋮ Isomorphisms and multipliers on second dual algebras of Banach algebras ⋮ Dual spaces and translation invariant means on group von Neumann algebras ⋮ Two open problems of Day and Wong on left thick subsets and left amenability ⋮ The cardinality of the set of left invariant means on topological semigroups ⋮ MULTIPLIERS ON THE SECOND DUAL OF ABSTRACT SEGAL ALGEBRAS ⋮ Counting topologically invariant means on \(L_\infty(G)\) and \(VN(G)\) with ultrafilters ⋮ Generalized notions of amenability. ⋮ Involutions and trivolutions in algebras related to second duals of group algebras ⋮ On character amenability of Banach algebras ⋮ Banach algebras on semigroups and on their compactifications ⋮ Extension of topological invariant means on a locally compact amenable group ⋮ On the set of topologically invariant means on an algebra of convolution operators on 𝐿^{𝑝}(𝐺) ⋮ When is an invariant mean the limit of a Følner net? ⋮ On the spectra of \(C^\ast\)-algebras of slowly oscillating functions on locally compact groups

Cites Work

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• Fixed-point theorems for compact convex sets
• The cardinality of the set of left invariant means on a left amenable semigroup
• Invariant means on a locally compact group
• Continuity of Arens multiplication on the dual space of bounded uniformly continuous functions on locally compact groups and topological semigroups
• The Exact Cardinality of the Set of Invariant Means on a Group
• The ideal structure of the Stone-Čech compactification of a group
• Constant Functions and Left Invariant Means on Semigroups
• On Topologically Invariant Means on a Locally Compact Group
• Exposed points of convex sets and weak sequential convergence

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