We prove that for every group G and any two sets I, J , the Brandt semigroup algebras l(B(I,G)) and l(B(J,G)) are Morita equivalent with respect to the Morita theory of selfinduced Banach algebras introduced by Grønbæk. As applications, we show that if G is an amenable group, then for a wide class of Banach l(B(I,G))-bimodules E, and every n > 0, the bounded Hochschild cohomology groups H(l(B(I...

Correspondence: [email protected] Department of Mathematics, University of Bonab 55517-61167 Bonab, Iran Abstract We introduce an iterative scheme for finding a common element of the set of solutions for systems of equilibrium problems and systems of variational inequalities and the set of common fixed points for an infinite family and left amenable semigroup of nonexpansive mappings i...

let a be a banach algebra. a is called ideally amenable if for every closed ideal i of a, the first cohomology group of a with coefficients in i* is trivial. we investigate the closed ideals i for which h1 (a,i* )={0}, whenever a is weakly amenable or a biflat banach algebra. also we give some hereditary properties of ideal amenability.

in this paper we study the existence of commuting regular elements, verifying the notion left (right) commuting regular elements and its properties in the groupoid g(n) . also we show that g(n) contains commuting regular subsemigroup and give a necessary and sucient condition for the groupoid g(n) to be commuting regular.

Suppose (X,σ) is a subshift, PX(n) is the word complexity function of X, and Aut(X) is the group of automorphisms of X. We show that if PX(n) = o(n 2/ log n), then Aut(X) is amenable (as a countable, discrete group). We further show that if PX(n) = o(n 2), then Aut(X) can never contain a nonabelian free semigroup (and, in particular, can never contain a nonabelian free subgroup). This is in con...

in the present paper, we consider biflatness of certain classes of semigroupalgebras. indeed, we give a necessary condition for a band semigroup algebra to bebiflat and show that this condition is not sufficient. also, for a certain class of inversesemigroups s, we show that the biflatness of ell^{1}(s)^{primeprime} is equivalent to the biprojectivity of ell^{1}(s).

A classical Kamae-Weiss theorem states that an increasing sequence (ni)i∈ℕ of positive lower density is normality preserving, i.e., has the property for any normal binary (bn)n∈ℕ, $${({n_i})_{i \in \mathbb{N}}}$$ normal, if and only a deterministic sequence. Given countable cancellative amenable semigroup G, Følner $${\cal F} = {({F_n})_{n \in}}$$ in we introduce notions preservation, determini...

The main purpose of this paper is to establish a relation between universality of certain P-compactifications of a semitopological semigroup and their corresponding enveloping semigroups. In particular, we show that if we take P to be the property that the enveloping semigroup of a compactification of a semitopological semigroup s is left simple, a group, or the trivial singleton semigroup, t...