We show that the group of bounded automatic automorphisms of a rooted tree is amenable, which implies amenability of numerous classes of groups generated by finite automata. The proof is based on reducing the problem to showing amenability just of a certain explicit family of groups (“Mother groups”) which is done by analyzing the asymptotic properties of random walks on these groups.

We introduce the notion of amenability for affine algebras. We characterize amenability by Følner-sequences, paradoxicality and the existence of finitely invariant dimension-measures. Then we extend the results of Rowen on ranks, from affine algebras of subexponential growth to amenable affine algebras. AMS Subject Classifications: 43A07, 16P90

We study the concept of α-amenability of commutative hypergroups K. We establish several characterizations of α-amenability by combining results of [1] and [2] and adding the Glicksberg-Reiter property. In addition, as examples compact K and discrete polynomial hypergroups on N0 are discussed. 2000 Mathematics Subject Classification: Primary 43A62, Secondary 46H25

Abstract. For any finite unital commutative idempotent semigroup S, a unital semilattice, we show how to compute the amenability constant of its semigroup algebra l(S), which is always of the form 4n+1. We then show that these give lower bounds to amenability constants of certain Banach algebras graded over semilattices. Our theory applies to certain natural subalgebras of Fourier-Stieltjes alg...

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...

We investigate the amenability of skew field extensions of the complex numbers. We prove that all skew fields of finite Gelfand-Kirillov transcendence degree are amenable. However there are both amenable and non-amenable finitely generated skew fields of infinite Gelfand-Kirillov transcendence degree. AMS Subject Classifications: 12E15, 43A07

motivated by an arens regularity problem, we introduce the concepts of matrix banach space and matrix banach algebra. the notion of matrix normed space in the sense of ruan is a special case of our matrix normed system. a matrix banach algebra is a matrix banach space with a completely contractive multiplication. we study the structure of matrix banach spaces and matrix banach algebras. then we...

In this paper, we introduce a new notion of strong pseudo-amenability for Banach algebras. We study some matrix Using tool, characterize [Formula: see text], provided that text] is uniformly locally finite inverse semigroup. As an application, show Brandt semigroup pseudo-amenable if and only amenable finite. give examples to the differences between other classical notions amenability.