Geodesic
On the “Third Definition” of the Topology on the Spectrum of a C*-Algebra
Canadian journal of mathematics, Tome 23 (1971) no. 3, pp. 445-450

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0. In [3], Fell introduced a topology on Rep (A,H), the collection of all non-null but possibly degenerate *-representations of the C*-algebra A on the Hilbert space H. This topology, which we will call the Fell topology, can be described by giving, as basic open neighbourhoods of π 0 ∈ Rep(A, H), sets of the form where the ai ∈ A, and the ξj ∈ H(π 0), the essential space of π 0 [4].A principal result of [3, Theorem 3.1] is that if the Hilbert dimension of H is large enough to admit all irreducible representations of A, then the quotient space Irr(A, H)/∼ can be identified with the spectrum (or “dual“) Â of A, in its hull-kernel topology. 
Gardner, L. Terrell. On the “Third Definition” of the Topology on the Spectrum of a C*-Algebra. Canadian journal of mathematics, Tome 23 (1971) no. 3, pp. 445-450. doi: 10.4153/CJM-1971-047-1
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[1] 1. Bichteler, K., A generalization to the non-separable case of Takesaki's duality theorem for C*-algebras, Invent. Math. 9 (1969), 89–98. Google Scholar

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[3] 3. Fell, J. M. G., C*-algebras with smooth dual, Illinois J. Math. 4 (1960), 221–230. Google Scholar

[4] 4. Fell, J. M. G., Weak containment and induced representations of groups, Can. J. Math. 14 (1962), 237–268. Google Scholar

[5] 5. Takesaki, M., A duality in the representation theory of C*-algebras, Ann. of Math. (2) 85 (1967), 370–382. Google Scholar

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