We prove the Moore and the Myhill property for strongly irreducible subshifts over right amenable and finitely right generated left homogeneous spaces with finite stabilisers. Both properties together mean that the global transition function of each big-cellular automaton with finite set of states and finite neighbourhood over such a subshift is surjective if and only if it is preinjective. Thi...

We show that the Gurarij space $\mathbb{G}$ has extremely amenable automorphism group. This answers a question of Melleray and Tsankov. also compute universal minimal flow group Poulsen simplex $\mathbb{P}$ we prove it consists canonical action on itself. Conley Törnquist. pointwise stabilizer any closed proper face is amenable. Similarly, biface unit ball dual (the Lusky simplex) These results...

It is an open problem whether an infinite-dimensional amenable Banach algebra exists whose underlying Banach space is reflexive. We give sufficient conditions for a reflexive, amenable Banach algebra to be finite-dimensional (and thus a finite direct sum of full matrix algebras). If A is a reflexive, amenable Banach algebra such that for each maximal left ideal L of A (i) the quotient A/L has t...

in this paper we study the relation between module amenability of θ - lau product a×θb and that of banach algebras a, b. we also discuss module biprojectivity of a×θb. as a consequent we will see that for an inverse semigroup s, l 1 (s) ×θ l 1 (s) is module amenable if and only if s is amenable.

Since 1929 when von Neumann [vN29] introduced the notion of an invariant mean on a group (and more generally on a G-set) there is a permanent interest in the study of the phenomenon known as amenability. Amenable objects like groups, semigroups, algebras, graphs, metric spaces, operator algebras etc. play an important role in different areas of mathematics. A big progress in understanding of th...

In this paper we describe proofs of the pointwise ergodic theorem and Shannon-McMillan-Breiman theorem for discrete amenable groups, along Følner sequences that obey some restrictions. These restrictions are mild enough so that such sequences exist for all amenable groups.

We generalize a theorem of Frey by giving sufficient conditions for a subsemigroup T of a cancellative left amenable semigroup S to be left amenable. In particular, we show that if S is left amenable and T does not contain a free subsemigroup on two generators, then T is left amenable as well.

we study topological von neumann regularity and principal von neumann regularity of banach algebras. our main objective is comparing these two types of banach algebras and some other known banach algebras with one another. in particular, we show that the class of topologically von neumann regular banach algebras contains all $c^*$-algebras, group algebras of compact abelian groups and cer...

Let $A$ be a Banach algebra and $E$ be a Banach $A$-bimodule then $S = A oplus E$, the $l^1$-direct sum of $A$ and $E$ becomes a module extension Banach algebra when equipped with the algebras product $(a,x).(a^prime,x^prime)= (aa^prime, a.x^prime+ x.a^prime)$. In this paper, we investigate $triangle$-amenability for these Banach algebras and we show that for discrete inverse semigroup $S$ with...