Related papers: Module Amenability for Semigroup Algebras

In this paper we prove a general convergence theorem for almost-additive set functions on unimodular, amenable groups. These mappings take their values in some Banach space. By extending the theory of epsilon-quasi tiling techniques, we set…

Extending M.\ Daws' definition of ultra-amenable Banach algebras, we introduce the notion of operator ultra-amenability for completely contractive Banach algebras. For a locally compact group $G$, we show that the operator ultra-amenability…

We study the connection between amenability, F{\o}lner conditions and the geometry of finitely generated semigroups. Using results of Klawe, we show that within an extremely broad class of semigroups (encompassing all groups, left…

We show that every group $H$ of at most exponential growth with respect to some left invariant metric admits a bi-Lipschitz embedding into a finitely generated group $G$ such that $G$ is amenable (respectively, solvable, satisfies a…

For a semigroup $S$ and a right $\mathbb{Z}[S]$-submodule $J\leq \mathbb{Z}[S]^n$, we study expansivity of the algebraic action of $S$ induced on the Pontryagin dual of $\mathbb{Z}[S]^n/J$. We completely determine the class of semigroups…

In this paper we prove that if (A,\pi) is an amenable Banach algebra and if \rho is another Banach algebra multiplication on A such that the difference between \rho and and \pi is less than 1/11, then (A, \rho) is also amenable.

Let $\A$ be a semisimple unital commutative Banach algebra. We say that a Banach $\A$-module $M$ is nice if every proper closed submodule of $M$ is contained in a closed submodule of $M$ of codimension 1. We provide examples of nice and…

Let $G$ be a locally compact group and $(\Phi,\Psi)$ a complimentary pair of Young functions. In this article, we consider the Banach algebra of $\Psi$-pseudomeasures $PM_\Psi(G)$ and the Orlicz Fig\`{a}-Talamanca Herz algebra $A_\Phi(G).$…

In this paper, we study the notion of $\phi$-biflatness for some Banach algebras, where $\phi$ is a non-zero multiplicative linear functional. We show that the Segal algebra $S(G)$ is left $\phi$-biflat if and only if $G$ is amenable. Also,…

In this paper, we introduce $p$-amenability, bounded $s$-symmetric approximate and $s$-symmetric virtual diagonals for a Banach algebra $\mathfrak{A}$ where $s$ is a non-zero element of algebraic center of $\mathfrak{A}$ that is denoted by…

In this paper, we introduce and investigate the concepts of cyclically weakly amenable and point amenable. Then, we compare these concepts with the concepts of weakly amenable and cyclically amenable and find the relation between them. For…

In this paper, among other things, we study those conditions under which the weighted semigroup algebra $\ell^1(S,\omega)$ is a dual Banach algebra with respect to predual $c_0(S)$. Some useful examples, illustrating the results, are also…

In this paper, we study the notion of $\phi$-biflatness, $\phi$-biprojectivity, approximate biprojectivity and Johnson pseudo-contractibility for a new class of Banach algebras. Using this class of Banach algebras we give some examples…

We consider the amenability of groupoids $G$ equipped with a group valued cocycle $c:G\to Q$ with amenable kernel $c^{-1}(e)$. We prove a general result which implies, in particular, that $G$ is amenable whenever $Q$ is amenable and if…

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 Folner…

Consider an algebraic semigroup $S$ and its closed subscheme of idempotents, $E(S)$. When $S$ is commutative, we show that $E(S)$ is finite and reduced; if in addition $S$ is irreducible, then $E(S)$ is contained in a smallest closed…

Different notions of amenability on hypergroups and their relations are studied. Developing Leptin's theorem for discrete hypergroups, we characterize the existence of a bounded approximate identity for hypergroup Fourier algebras. We study…

Let $k$ be an algebraically closed field of characteristic zero, and $k[[z]]$ the ring of formal power series over $k$. We provide several characterizations of right amenable finitely generated subsemigroups of $z^2k[[z]]$ with the…

We prove the following two results. First, the isometry semigroup of a unital properly infinite nuclear C*-algebra is right amenable. Second, the unitary group of a unital simple monotracial C*-algebra whose tracial GNS representation is…

Character inner amenability for certain class of Banach algebras consist of projective tensor product $A\hat{\otimes}B$, Lau product $A\times_\theta B$ and module extension $A\oplus X$ are investigated. Some illuminating examples are also…