For a locally compact group G, let A(G) denote its Fourier algebra and Ĝ its dual object, i.e. the collection of equivalence classes of unitary representations of G. We show that the amenability constant of A(G) is less than or equal to sup{deg(π) : π ∈ Ĝ} and that it is equal to one if and only if G is abelian.

it was shown in [a. azimifard, e. samei, n. spronk, jfa 256 (2009)] that the zl-amenability constant of a finite group is always at least~$1$, with equality if and only if the group is abelian. it was also shown in [a. azimifard, e. samei, n. spronk, op cit.] that for any finite non-abelian group this invariant is at least $301/300$, but the proof relies crucially on a deep result of d. a. ride...

Abstract. For any finite unital commutative idempotent semigroup S, a unital semilattice, we show how to compute the amenability constant of its semigroup algebra l(S), which is always of the form 4n+1. We then show that these give lower bounds to amenability constants of certain Banach algebras graded over semilattices. Our theory applies to certain natural subalgebras of Fourier-Stieltjes alg...

In this paper, we investigate, for a locally compact groupG, the operator amenability of the Fourier-Stieltjes algebra B(G) and of the reduced Fourier-Stieltjes algebra Br(G). The natural conjecture is that any of these algebras is operator amenable if and only if G is compact. We partially prove this conjecture with mere operator amenability replaced by operator C-amenability for some constant...

in this paper we introduce two symmetric variants of amenability, symmetric module amenability and symmetric connes amenability. we determine symmetric module amenability and symmetric connes amenability of some concrete banach algebras. indeed, it is shown that $ell^1(s)$ is  a symmetric $ell^1(e)$-module amenable if and only if $s$ is amenable, where $s$ is an inverse semigroup with subsemigr...

Abstract We show that if a locally compact group $G$ is non-abelian, then the amenability constant of its Fourier algebra $\geq 3/2$, extending result [9] who proved this holds for finite non-abelian groups. Our lower bound, which known to be best possible, improves on results by previous authors and answers question raised [16]. To do this, we study minorant constant, related anti-diagonal in ...

In this paper we introduce two symmetric variants of amenability, symmetric module amenability and symmetric Connes amenability. We determine symmetric module amenability and symmetric Connes amenability of some concrete Banach algebras. Indeed, it is shown that $ell^1(S)$ is  a symmetric $ell^1(E)$-module amenable if and only if $S$ is amenable, where $S$ is an inverse semigroup with subsemigr...

In this paper, we introduce a concept of an evacuation scheme on the Cayley graph infinite finitely generated group. This is collection simple paths bringing all vertices to infinity. We impose restriction that every edge can be used uniformly bounded number times in scheme. An easy observation shows existence such equivalent non-amenability A special case happens if only once. These schemes ar...

We define the isoperimetric constant for any locally finite metric space and we study the property of having isoperimetric constant equal to zero. This property, called Small Neighborhood property, clearly extends amenability to any locally finite space. Therefore, we start making a comparison between this property and other notions of amenability for locally finite metric spaces that have been...