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On the Mackey Borel Structure

Published online by Cambridge University Press:  20 November 2018

L. Terrell Gardner
L. Terrell Gardner*
Affiliation:
University of Toronto, Toronto, Ontario
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Let A be a C*-algebra and a Hilbert space which is infinite dimensional and of Hilbert dimension ≧ dim π for all π ∈ Â. Suppose that the set Irr of all non-null *-representations π of A on , irreducible on the essential space , is given the relative strong topology as a subspace of Rep [2; 4; 6]. That is, the topology is that of simple convergence in with the strong topology. Finally, let ∼ denote equivalence of representations in Irr implemented by partial isometries in if and only if there exists a partial isometry with vv* ⊃ H(π1) and v*v ⊃ H(π2) satisfying π2(a) = v*π1(a)v for all a ∈ A.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 23 , Issue 4 , August 1971 , pp. 674 - 678
Copyright
Copyright © Canadian Mathematical Society 1971

References

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