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Pure states with the restriction property


Author: Bruce A. Barnes
Journal: Proc. Amer. Math. Soc. 33 (1972), 491-494
MSC: Primary 46L05
DOI: https://doi.org/10.1090/S0002-9939-1972-0295089-X
MathSciNet review: 0295089
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Abstract: Conditions are given which imply that a pure state of a $ {B^\ast}$-algebra A restricts to a pure state of some maximal commutative $ ^\ast$-subalgebra of A.


References [Enhancements On Off] (What's this?)

  • [1] J. F. Aarnes and R. V. Kadison, Pure states and approximate identities, Proc. Amer. Math. Soc. 21 (1969), 749-752. MR 39 #1980. MR 0240633 (39:1980)
  • [2] C. A. Akemann, Approximate units and maximal Abelian $ {C^\ast}$-subalgebras, Pacific J. Math. 33 (1970), 543-550. MR 41 #9001. MR 0264406 (41:9001)
  • [3] J. Dixmier, Les $ {C^\ast}$-algèbres et leurs représentations, Cahiers Scientifiques, fasc. 29, Gauthier-Villars, Paris, 1964. MR 30 #1404. MR 0171173 (30:1404)
  • [4] R. V. Kadison and I. M. Singer, Extensions of pure states. Amer. J. Math. 81 (1959), 383-400. MR 23 #A1243. MR 0123922 (23:A1243)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0295089-X
Keywords: $ {B^\ast}$-algebra, pure state, maximal commutative $ ^\ast$-subalgebra
Article copyright: © Copyright 1972 American Mathematical Society

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