let g be a locally compact group, and let ω be a weight on g. we show that the weightedmeasure algebra m(g,ω) is amenable if and only if g is a discrete, amenable group andsup{ω(g) ω(g−1) : g ∈ g} < ∞, where ω(g) ≥ 1 (g ∈ g) .

We show that the groups of finite energy loops and paths (that is, those Sobolev class H 1 ) with values in a compact connected Lie group, as well their central extensions, satisfy an amenability-like property: they admit left-invariant mean on space bounded functions uniformly continuous regard to metric. Every strongly unitary representation π such group (which we call skew-amenable) has conj...

Let G be a locally compact amenable group, TLIM ( ) the topological left-invariant means on , and 0 limit points of Følner-nets. I show that = unless is σ -compact non-unimodular, in which case ≠ . This improves 1970 result Chou 2009 Hindman Strauss. consider analogous problem for non-topological means, give short construction net converging to invariance “weakly but not strongly,” simplifying ...

Nongalenic intradural arteriovenous fistulas, although uncommon, are clinically important. Choosing the appropriate therapeutic approach has been a controversial issue within the last decade.A 15-year-old male was presented with a calcified nongalenic arteriovenous fistula in the left parietal region, supplied by the left middle cerebral artery, and draining into the left lateral sinus. The pat...

let a be a banach algebra and e be a banach a-bimodule then s = a  e, the l1-direct sum of a and e becomes a module extension banach algebra when equipped with the algebras product (a; x):(a′; x′) = (aa′; a:x′ + x:a′). in this paper, we investigate △-amenability for these banach algebras and we show that for discrete inverse semigroup s with the set of idempotents es, the module extension bana...

In this paper, we consider ultrapowers of Banach algebras as and the product $${{\bigcirc }_{{(J,\mathcal{U})}}}$$ on second dual algebras. For a algebra A, show that if there is continuous derivation from A into itself, then (A**, ) it. Moreover, X**, where X A-bimodule, ultrapower X; i.e., $${{(X)}_{\mathcal{U}}}$$ . Ultra (character) amenability investigated it will be shown every inner, ult...

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...