Abstract Consider a positive Borel measure on locally compact group. We define notion of uniform density for such measure, which is based group invariant introduced by Leptin in 1966. then restrict to unimodular amenable groups and translation bounded measures. In that case our coincides with the well-known Beurling from Fourier analysis, also known as Banach dynamical systems theory. use densi...

Amenability is a geometric property of convex cones that stronger than facial exposedness and assists in the study error bounds for conic feasibility problems. In this paper we establish numerous properties amenable investigate relationships between amenability other cones, such as niceness projectional exposure. We show compact slice closed cone equivalent to cone, prove several results on pre...

BACKGROUND Although advances in early detection and treatment of cancer improve overall population survival, these advances may not benefit all population groups equally and may heighten racial/ethnic differences in survival. METHODS We identified cancer cases in the Surveillance, Epidemiology and End Results program, who were ages > or = 20 years and diagnosed with one invasive cancer in 199...

 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...