let $a$ be an arbitrary banach algebra and $varphi$ a homomorphism from $a$ onto $bbb c$. our first purpose in this paper is to give some equivalent conditions under which guarantees a $varphi$-mean of norm one. then we find some conditions under which there exists a $varphi$-mean in the weak$^*$ cluster of ${ain a; |a|=varphi(a)=1}$ in $a^{**}$.

We establish a close link between the amenability property of a unitary representation π of a groupG (in the sense of Bekka) and the concentration property (in the sense of V. Milman) of the corresponding dynamical system (Sπ , G), where SH is the unit sphere the Hilbert space of representation. We prove that π is amenable if and only if either π contains a finite-dimensional subrepresentation ...

For horocyclic products of percolation subtrees of regular trees, we show almost sure amenability. Under a symmetry condition concerning the growth of the two percolation trees, we show the existence of an increasing Følner sequence (which we call strong amenability).

Abstract International economic law is peculiar. It claims universal character, yet eschews engagement with many, if not all, the racialised features of global political economy. Its scholars mostly ignore imperialism, colonialism, and capitalism; they exclude slavery, predation, racism altogether. In following article, we draw upon Walter Rodney’s dialectics development to offer a racial capit...

Let A be a unital amenable A∗-algebra, or a unital commutative hermitian Banach ∗-algebra. We show that if ρ : A → B(H) is a bounded homomorphism, then ρ is completely bounded and ‖ρ‖cb ≤ ‖ρ‖2. Mathematics Subject Classification: 46L07; 46k05