Amenability of any of the algebras described in the title is known to force them to be finite-dimensional. The analogous problems for approximate amenability have been open for some years now. In this article we give a complete solution for the first two classes, using a new criterion for showing that certain Banach algebras without bounded approximate identities cannot be approximately amenabl...

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It is shown that every bundle Σ → M of complex spinor modules over the Clifford bundle Cl(g) of a Riemannian space (M,g) with local model (V, h) is associated with an lpin (“Lipschitz”) structure on M , this being a reduction of the O(h)-bundle of all orthonormal frames on M to the Lipschitz group Lpin(h) of all automorphisms of a suitably defined spin space. An explicit construction is given o...

We give the regularization for fractional integral by delta sequence and apply it to obtain existence-uniqueness theorems in Colombeau algebras for nonlinear equations with singularities: nonlinear system of integral equations with polar kernel and nonlinear parabolic equations (of ordinary type, with nonlinear conservative term and with Schrödinger kernel) with strongly singular initial data a...

We show how to make precise the vague idea that for compact metric spaces that are close together for Gromov– Hausdorff distance, suitable vector bundles on one metric space will have counterpart vector bundles on the other. Our approach employs the Lipschitz constants of projection-valued functions that determine vector bundles. We develop some computational techniques, and we illustrate our i...

This text is a further elaboration of the previous research report [5]. Graded properties of binary and unary connectives valued in MTL4-algebras are studied in the framework of Fuzzy Class Theory (or higher-order fuzzy logic) FCT, which serves as a tool for easy derivation of graded theorems. The properties studied include graded monotonicity, a generalized Lipschitz property, commutativity, a...

In contrast to the usual Lipschitz seminorms associated to ordinary metrics on compact spaces, we show by examples that Lipschitz seminorms on possibly non-commutative compact spaces are usually not determined by the restriction of the metric they define on the state space, to the extreme points of the state space. We characterize the Lipschitz norms which are determined by their metric on the ...

We prove that allKK-homology classes of the stable (and unstable) Ruelle algebra a Smale space have explicit Fredholm module representatives ...

we study topological von neumann regularity and principal von neumann regularity of banach algebras. our main objective is comparing these two types of banach algebras and some other known banach algebras with one another. in particular, we show that the class of topologically von neumann regular banach algebras contains all $c^*$-algebras, group algebras of compact abelian groups and cer...