For a Banach algebra $fA$, we introduce ~$c.c(fA)$, the set of all $phiin fA^*$ such that $theta_phi:fAto  fA^*$ is a completely continuous operator, where $theta_phi$ is defined by $theta_phi(a)=acdotphi$~~ for all $ain fA$. We call $fA$, a completely continuous Banach algebra if $c.c(fA)=fA^*$. We give some examples of completely continuous Banach algebras and a sufficient condition for an o...

Abstract Amenable actions of locally compact groups on von Neumann algebras are investigated by exploiting the natural module structure crossed product over Fourier algebra acting group. The resulting characterization injectivity for products generalizes a result Anantharaman-Delaroche discrete groups. $C^*$ -algebras in same way, and amenability action is related to nuclearity corresponding pr...

in this paper among many other things we prove that the topological left amenability and left amenability of a weighted hypergroup (k, ?) are equivalent. for a normal subgroup h of k, we define a weight function ?? on kih and obtain connection between left amenability of (k, ?) and (k|h, ??). let h be a compact subhypergroup of k. we define the weight function on k||h and obtain connection betw...

Consider a measure-preserving action Γ y (X,μ) of a countable group Γ and a measurable cocycle α : X × Γ → Aut(Y ) with countable image, where (X,μ) is a standard Lebesgue space and (Y, ν) is any probability space. We prove that if the Koopman representation associated to the action Γ y X is non-amenable, then there does not exist a countable-to-one Borel homomorphism from the orbit equivalence...

We report reactions of LiNacNac and NacNacMg(TMP) with common organic substrates (TMP = 2,2,6,6-tetramethylpiperidide). Using bulky β-diketiminate compound, NacNac (Me, Dipp) we have trapped metallated intermediates amenable to X-ray crystallographic study. acetone produced the NacNac-free hexameric diacetone alkoxide [{LiO(MeC(=O)CH2C(Me)2}6]; whereas pinacolone gave simple monomeric donor-acc...

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...