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Mackey Borel Structure for the Quasi-Dual of a Separable C*-Algebra

Published online by Cambridge University Press:  20 November 2018

Herbert Halpern
Herbert Halpern*
Affiliation:
University of Cincinnati, Cincinnati, Ohio
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Let A be a separable C*-algebra. Two representations π and π1 of A on the Hilbert spaces H and H1, respectively are said to be quasi-equivalent (denoted by π ~ π1) if projections of H ⊕ H1 on the invariant subspaces H and H1 of (π ⊕ π1)(A) have the same central support in the commutant (π ⊕ π1) (A)′ of (π ⊕ π1) (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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 3 , June 1974 , pp. 621 - 628
Copyright
Copyright © Canadian Mathematical Society 1974

References

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