We propose a definition of a “C-Eberlein” algebra, which is a weak form of a C-bialgebra with a sort of “unitary generator”. Our definition is motivated to ensure that commutative examples arise exactly from semigroups of contractions on a Hilbert space, as extensively studied recently by Spronk and Stokke. The terminology arises as the Eberlein algebra, the uniform closure of the Fourier-Stiel...

The Stone-Čech compactification of discrete semigroups is a tool of central importance in several areas of mathematics, and has been studied extensively. We think of the Stone-Čech compactification of a discrete abelian semigroup G as the set βG of ultrafilters on G, where the point x ∈ G is identified with the principal ultrafilter {A ⊆ G ∣∣x ∈ A}, and the basic open sets are those of the form...

Abstract We introduce the notion of an introverted Boolean algebra $\mathcal{B}$ closed-and-open subsets a topological group G, show that associated Stone space $(\nu_{\mathcal{B}} \nu_{\mathcal{B}})$ is totally disconnected semigroup compactification G and every takes this form. identify study universal compactification, semitopological G. Our main results are obtained independently Gelfand th...

For any affine semigroup S, the set S∪{∞} has a natural structure; additionally, if S is endowed with discrete topology, then can be studied as one-point compactification of S. In this article, we study derivations on algebra C[S∪{∞}] in relation to C[S] considering metrizable topology induced by S∪{∞}.

We consider weighted graphs with an infinite set of vertices. We show that boundedness of all functions of finite energy can be seen as a notion of ‘relative compactness’ for such graphs and study sufficient and necessary conditions for this property in terms of various metrics. We then equip graphs satisfying this property with a finite measure and investigate the associated Laplacian and its ...

We examine some peculiarities of the subset of lattice preserving elements in a pseudo-Euclidean group, when the lattice under consideration contains a lightlike vector, or more generally, when the restriction of a pseudo-Euclidean metric to the real linear enveloppe of the lattice is not definite. For the case of a Lorentzian metric, it is shown in detail that the isometry group of the spaceti...