| dc.description.abstract | separation properties of the fell topology, on the spectrum g of a locally compact group
g, characterize important properties of g. we will develop three equivalent ways to
describe the fell topology on the spectrum â of any c* algebra a. specifically, we
show that both the relative weak*-topology on p(a), the set of pure states of a, and
the jacobson topology on prim(a), the set of all primative ideals on a, can be mapped
onto â so that both topologies agree with the fell topology. we will also study the
correspondences, both between the set of strongly continuous unitary representations
of g and the irreducible representations of the group c*-algebra g*(g), and between
the continuous functions of positive type on g and the set of pure states of g*(g). as
well, we give a survey of results outlining the characterization of g by simple separation
properties of the fell topology on g. | |
