On the spectrum G of a locally compact group G
Whitfield, John Brian
Master of Arts
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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.