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...

 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...