A topological group G is called extremely amenable if every continuous action of G on a compact space has a fixed point. This concept is linked with geometry of high dimensions (concentration of measure). We show that a von Neumann algebra is approximately finite-dimensional if and only if its unitary group with the strong topology is the product of an extremely amenable group with a compact gr...

begin{abstract} in this paper, we introduce an iterative method for amenable semigroup of non expansive mappings and infinite family of non expansive mappings in the frame work of hilbert spaces. we prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality, which is the optimality condition for a minimization problem. the results present...

We will give a brief account of (topological) amenable actions and exactness for countable discrete groups. The class of exact groups contains most of the familiar groups and yet is manageable enough to provide interesting applications in geometric topology, von Neumann algebras and ergodic theory. Mathematics Subject Classification (2000). Primary 46L35; Secondary 20F65, 37A20, 43A07.

In the present paper we construct the first examples of finitely generated non–amenable groups whose left regular representations are not uniformly isolated from the trivial representation.

A locally compact group G is amenable if and only if it has Reiter’s property (Pp) for p = 1 or, equivalently, all p ∈ [1,∞), i.e., there is a net (mα)α of non-negative norm one functions in L(G) such that limα supx∈K ‖Lx−1mα − mα‖p = 0 for each compact subset K ⊂ G (Lx−1mα stands for the left translate of mα by x ). We extend the definitions of properties (P1) and (P2) from locally compact gro...

We construct  a noncommutative analog of additive functional equations on discrete quantum semigroups and show that this noncommutative functional equation has Hyers-Ulam stability on amenable discrete quantum semigroups. The discrete quantum semigroups that we consider in this paper are in the sense of van Daele, and the amenability is in the sense of Bèdos-Murphy-Tuset. Our main result genera...

This paper continues the investigation of the rst author begun in part one. The hereditary properties of n-homomorphism amenability for Banach algebras are investigated and the relations between n-homomorphism amenability of a Banach algebra and its ideals are found. Analogous to the character amenability, it is shown that the tensor product of two unital Banach algebras is n-homomorphism amena...

For independent density p site percolation on the (transitive non-amenable) graph T b Z, where T b is a homogeneous tree of degree b + 1, and b is supposed to be large, it is shown that for p = p u = inffp: a.s. there is a unique innnite clusterg there are a.s. innnitely many inn-nite clusters. This contrasts with a recent result of Benjamini and Schramm, according to whom for transitive non-am...

In the present paper, the concepts of module (uniform) approximate amenability and contractibility of Banach algebras that are modules over another Banach algebra, are introduced. The general theory is developed and some hereditary properties are given. In analogy with the Banach algebraic approximate amenability, it is shown that module approximate amenability and contractibility are the same ...

Let Γ be a finitely generated, amenable group. We prove that if Γ has a nontrivial, orientation-preserving action on the real line, then Γ has an infinite, cyclic quotient. (The converse is obvious.) This implies that if Γ has a faithful action on the circle, then some finite-index subgroup of Γ has the property that all of its nontrivial finitely generated subgroups have infinite, cyclic quoti...