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.

Xenopus egg cytoplasmic extracts have been used to study a variety of complex cellular processes. Given their amenability to biochemical manipulation and physiological balance of regulatory proteins, these extracts are an ideal system to dissect signal transduction pathways leading to actin assembly. We have developed methods to study Cdc42 and PI(4,5)P2-induced actin assembly in Xenopus egg ex...

Forces generated by cells play a vital role in many cellular processes like cell spreading, motility, differentiation and apoptosis. Understanding the mechanics of single cells is essential to delineate the link between cellular force generation/sensing and function. MEMS sensors, because of their small size and fine force/displacement resolution, are ideal for force and displacement sensing at...

The soil nematode, Caenorhabditis elegans, occupies a central place in the short history of microRNA (miRNA) research. The converse is also true: miRNAs have emerged as key regulatory components in the life cycle of the worm, as well as numerous other organisms. Since the landmark discovery in 1993 of the first miRNA gene, lin-4, several other miRNAs have been characterized in detail in C. eleg...

The paper has two objectives. On the one hand, we study left Haar null sets—a measure theoretic notion of smallness on Polish, not necessarily locally compact, groups. On the other hand, we introduce and investigate two classes of Polish groups which are closely related to this notion and to amenability. We show that left Haar null sets form a σ-ideal and have the Steinhaus property on Polish g...

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.