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Factor Representations and Factor States on a C*-Algebra

Published online by Cambridge University Press:  20 November 2018

James A. Schoen
James A. Schoen*
Affiliation:
University of Wisconsin, La Crosse, Wisconsin
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Let A be a C*-algebra and H a Hilbert space of large enough (infinite at least) dimension so that every πƒ, where ƒ is a factor state on A, can be unitarily represented on H. Let Fac (A, H) denote the set of all factor representations of A on H. If π is in Fac (A, H) we call its essential subspace the smallest, closed, vector subspace KoiH such that π (A ) is null on H Θ K. We define Fac∞(A, H) to be the set of elements in Fac (A, H) whose essential subspace is H.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 1 , 01 February 1976 , pp. 130 - 134
Copyright
Copyright © Canadian Mathematical Society 1976

References

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
2. Dixmier, J., Les C*-algebres et leurs representations, Cahiers Scientifiques, fasc. 29 (Gauthier Villars, Paris, 1969).Google Scholar
3. Halpern, H., Open projections and Borel structures for C*-algebras, Pacific J. Math. SO (1974), 81–98.Google Scholar