General non-commutative locally compact locally Hausdorff Stone duality

P-Amenable Locally Compact Hypergroups

Non-commutative locally convex measures

We study weakly compact operators from a C∗-algebra with values in a complete locally convex space. They constitute a natural non-commutative generalization of finitely additive vector measures with values in a locally convex space. Several results of Brooks, Sâıto and Wright are extended to this more general setting. Building on an approach due to Sâıto and Wright, we obtain our theorems on no...

A Hausdorff Topology for the Closed Subsets of a Locally Compact Non-hausdorff Space

In the structure theory of C*-algebras an important role is played by certain topological spaces X which, though locally compact in a certain sense, do not in general satisfy even the weakest separation axiom. This note is concerned with the construction of a compact Hausdorff topology for the space G(X) of all closed subsets of such a space X. This construction occurs naturally in the theory o...

A Non-commutative Generalization of Stone Duality

We prove that the category of boolean inverse monoids is dually equivalent to the category of boolean groupoids. This generalizes the classical Stone duality between boolean algebras and boolean spaces. As an instance of this duality, we show that the boolean inverse monoid Cn associated with the Cuntz groupoid Gn is the strong orthogonal completion of the polycyclic (or Cuntz) monoid Pn. The g...

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 .