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

This paper identifies nine characteristics of road safety problems that are all in principle amenable to numerical measurement. The nine characteristics identified are: 1. Magnitude 2. Severity 3. Externality 4. Inequity 5. Complexity 6. Spatial dispersion 7. Temporal stability 8. Perceived urgency 9. Amenability to treatment. The purpose of identifying these dimensions and of trying to measure...

We consider the isometry group of infinite dimensional separable hyperbolic space with its Polish topology. This topology is given by pointwise convergence. For non-locally compact groups, some striking phenomena like automatic continuity or extreme amenability may happen. Our leading idea to compare this topological usual Lie groups on one side and non-Archimedean $\mathcal{S}_\infty$, all per...

In this paper we study the relation between module amenability of $theta$-Lau product $A×_theta B$ and that of Banach algebras $A, B$. We also discuss module biprojectivity of $A×theta B$. As a consequent we will see that for an inverse semigroup $S$, $l^1(S)×_theta l^1(S)$ is module amenable if and only if $S$ is amenable.

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.

The purpose of this article is to connect the notion of the amenability of a discrete group with a new form of structural Ramsey theory. The Ramsey theoretic reformulation of amenability constitutes a considerable weakening of the Følner criterion. As a by-product, it will be shown that in any non amenable group G, there is a subset E of G such that no finitely additive probability measure on G...

There is a word metric d on countably generated free group Γ such that (Γ, d) does not admit a coarse uniform imbedding into a Hilbert space.

— The minimum mean-squared-error (MMSE) linear multiuser detector [1–2] is popular because of its good performance and amenability to adaptive implementation. However , there are circumstances in which the linear detector that minimizes bit-error rate (BER) can significantly outperform the MMSE detector. We propose a low-complexity adaptive algorithm for approximating the minimum-BER linear mul...