Geodesic
Mackey Borel Structure for the Quasi-Dual of a Separable C*-Algebra
Canadian journal of mathematics, Tome 26 (1974) no. 3, pp. 621-628

Voir la notice de l'article provenant de la source Cambridge University Press

Let A be a separable C*-algebra. Two representations π and π1 of A on the Hilbert spaces H and H 1, respectively are said to be quasi-equivalent (denoted by π ~ π 1) if projections of H ⊕ H 1 on the invariant subspaces H and H 1 of (π ⊕ π 1)(A) have the same central support in the commutant (π ⊕ π 1) (A)′ of (π ⊕ π 1) (A), or equivalently, if there is an isomorphism φ of π(A)′′ onto π1 (A)′′ such that φ(π(x)) = π(x) for all x ∊ A (cf. [5, § 5]). A representation π of A is said to be a factor representation if the center of π(A)′′ consists of scalar multiples of the identity. 
Halpern, Herbert. Mackey Borel Structure for the Quasi-Dual of a Separable C*-Algebra. Canadian journal of mathematics, Tome 26 (1974) no. 3, pp. 621-628. doi: 10.4153/CJM-1974-059-9
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