A cancellative amenable ascending union of nonamenable semigroups
We construct an example of a cancellative amenable semigroup which is the ascending union of semigroups, none of which are amenable.
A categorical approach to invariant means and fixed point properties.
A descriptive view of unitary group representations
In this paper, we will study the relative complexity of the unitary duals of countable groups. In particular, we will explain that if and are countable amenable non-type I groups, then the unitary duals of and are Borel isomorphic.
A multiplier counter-example for mixed-norm spaces
A Note on the Amenable Subgroups of PSL (2, R).
A notion of open generalized morphism that carries amenability.
A Poisson formula for harmonic projections
A property for locally convex *-algebras related to property (T) and character amenability
For a locally convex *-algebra A equipped with a fixed continuous *-character ε (which is roughly speaking a generalized F*-algebra), we define a cohomological property, called property (FH), which is similar to character amenability. Let be the space of continuous functions with compact support on a second countable locally compact group G equipped with the convolution *-algebra structure and a certain inductive topology. We show that has property (FH) if and only if G has property (T). On...
A Remark on Continuity of Translation Invariant Functionals on L... (G) for Compact Lie Groups G.
Absolut stetige Maße auf lokalkompakten Halbgruppen.
Action of topological semigroups, invariant means, and fixed points
Amenability and locally compact semigroups.
Amenability and Ramsey theory
The purpose of this article is to connect the notion of the amenability of a discrete group with a new form of structural Ramsey theory. The Ramsey-theoretic reformulation of amenability constitutes a considerable weakening of the Følner criterion. As a by-product, it will be shown that in any non-amenable group G, there is a subset E of G such that no finitely additive probability measure on G measures all translates of E equally. The analysis of discrete groups will be generalized to the setting...
Amenability and unique ergodicity of automorphism groups of Fraïssé structures
In this paper we consider those Fraïssé classes which admit companion classes in the sense of [KPT]. We find a necessary and sufficient condition for the automorphism group of the Fraïssé limit to be amenable and apply it to prove the non-amenability of the automorphism groups of the directed graph S(3) and the boron tree structure T. Also, we provide a negative answer to the Unique Ergodicity-Generic Point problem of Angel-Kechris-Lyons [AKL]. By considering , where is the countably infinite-dimensional...
Amenability and weak amenability of l¹-algebras of polynomial hypergroups
We investigate amenability and weak amenability of the l¹-algebra of polynomial hypergroups. We derive conditions for (weak) amenability adapted to polynomial hypergroups and show that these conditions are often not satisfied. However, we prove amenability for the hypergroup induced by the Chebyshev polynomials of the first kind.
Amenability, extreme amenability, model-theoretic stability, and dependence property in integral logic
This paper has three parts. First, we study and characterize amenable and extremely amenable topological semigroups in terms of invariant measures using integral logic. We prove definability of some properties of a topological semigroup such as amenability and the fixed point on compacta property. Second, we define types and develop local stability in the framework of integral logic. For a stable formula ϕ, we prove definability of all complete ϕ-types over models and deduce from this the fundamental...
Amenability in Group Algebras and Banach Algebras.
Amenability induced by amenable homomorphlc images.
Amenability of linear-activity automaton groups
We prove that every linear-activity automaton group is amenable. The proof is based on showing that a random walk on a specially constructed degree 1 automaton group – the mother group – has asymptotic entropy 0. Our result answers an open question by Nekrashevych in the Kourovka notebook, and gives a partial answer to a question of Sidki.
Amenability, unimodularity, and the spectral radius of random walks on finite graphs.