Related papers: A brief introduction to amenable equivalence relat…
A brief introduction into Idempotent Mathematics and an idempotent version of Interval Analysis are presented. Some applications are discussed.
We formulate some problems and conjectures about semigroups of rational functions under composition. The considered problems arise in different contexts, but most of them are united by a certain relationship to the concept of amenability.
This paper deals with the comparison of two common types of equivalence groups of differential equations, and this gives rise to a number of results presented in the form of theorems. It is shown in particular that one type can be…
The notions of module pseudo-amenable and module pseudo-contractible Banach algebras are introduced. For a Banach algebra with bounded approximate identity, module pseudo-amenability and module approximate amenability are the same…
This is a brief and gentle introduction, aimed at graduate students, to the subject of model subspaces of the Hardy space.
We present an introduction to weak amenability for locally compact groups, and a survey of some of the most important results regarding this property.
A standard tool for classifying the complexity of equivalence relations on $\omega$ is provided by computable reducibility. This reducibility gives rise to a rich degree structure. The paper studies equivalence relations, which induce…
We show that for a Banach algebra $A$ with a bounded approximate identity, the amenability of the projective tensor product of A with A, the amenability of the projective tensor product of A with A^{op}and the amenability of A are…
As an extension of positive or almost positive diagrams and links, we introduce a notion of successively almost positive diagrams and links, and good successively almost positive diagrams and links. We review various properties of positive…
In this paper, we show that there is a net for amenable transformation groups like F{\o}lner net for amenable groups and investigate amenability of a transformation group constructed by semidirect product of groups. We introduce inner…
In this paper induced U-equivalence spaces are introduced and discussed. Also the notion of U-equivalently open subsets of a U-equivalence space and U-equivalently open functions are studied. Finally, equivalently uniformisable topological…
This text surveys classical and recent results in the field of amenability of groups, from a combinatorial standpoint. It has served as the support of courses at the University of G\"ottingen and the \'Ecole Normale Sup\'erieure. The goals…
In this note we briefly survey and propose some open problems related to isoparametric theory.
This paper gives a short introduction into the metric theory of spaces with dilations.
We look at equivalence relations on the set of models of a theory -- MERs, for short -- such that the class of equivalent pairs is itself an elementary class, in a language appropriate for pairs of models. We provide many examples of…
In this paper, a group is called weakly amenable if its left regular representation is not uniformly isolated from the trivial representation. First examples of finitely generated non-amenable weakly amenable groups are constructed.
In this paper the concepts of character contractibility, approximate character amenability (contractibility) and uniform approximate character amenability (contractibility) are introduced. We are concerned with the relations among the…
We discuss applications of minimal surfaces to comparison geometry.
We extend some recent results about bounded invariant equivalence relations and invariant subgroups of definable groups: we show that type-definability and smoothness are equivalent conditions in a wider class of relations than heretofore…
We point out a simple characterisation of topological amenability in terms of bounded cohomology, following Johnson's reformulation of amenability.