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

C. Deninger produced a unified description of the local factors at arithmetic infinity and at the finite places where the local Frobenius acts semi-simply, in the form of a Ray–Singer determinant of a “logarithm of Frobenius” Φ on an infinite dimensional vector space (the archimedean cohomology H · ar(X) at the archimedean places, cf. [11]). The first author gave a cohomological interpretation ...

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.