Homogeneous functionals on locally compact cones

On groups with locally compact asymptotic cones

We show how a recent result of Hrushovsky [6] implies that if an asymptotic cone of a finitely generated group is locally compact, then the group is virtually nilpotent. Let G be a group generated by a finite set X. Then G can be considered as a metric space where dist(g, h) is the length of a shortest word on X ∪X−1 representing g−1h. Let ω be a non-principal ultrafilter on N, i.e. a function ...

Arveson Spectrum On Locally Compact Hypergroups

In this paper we study the concept of Arveson spectrum on locally compact hypergroups and for an important class of compact countable hypergroups . In thiis paper we study the concept of Arveson spectrum on locally compact hypergroups and develop its basic properties for an important class of compact countable hypergroups .

On component extensions locally compact abelian groups

Let $pounds$ be the category of locally compact abelian groups and $A,Cin pounds$. In this paper, we define component extensions of $A$ by $C$ and show that the set of all component extensions of $A$ by $C$ forms a subgroup of $Ext(C,A)$ whenever $A$ is a connected group. We establish conditions under which the component extensions split and determine LCA groups which are component projective. ...

Bracket Products on Locally Compact Abelian Groups

We define a new function-valued inner product on L2(G), called ?-bracket product, where G is a locally compact abelian group and ? is a topological isomorphism on G. We investigate the notion of ?-orthogonality, Bessel's Inequality and ?-orthonormal bases with respect to this inner product on L2(G).

Some Results on Boundedness in Locally Convex Cones