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Proceedings of the American Mathematical Society

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On vector states and separable $ C\sp*$-algebras


Author: Joel Anderson
Journal: Proc. Amer. Math. Soc. 65 (1977), 62-64
MSC: Primary 46L05
DOI: https://doi.org/10.1090/S0002-9939-1977-0448090-1
MathSciNet review: 0448090
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Abstract: It is proved that the set of states on a separable $ {C^\ast}$-subalgebra of the Calkin algebra may be simultaneously extended to a set of equivalent, orthogonal, pure states on the Calkin algebra.


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

  • [1] J. Anderson, Extreme points in sets of positive linear maps on $ \mathcal{B}(\mathcal{H})$ (to appear).
  • [2] J. Glimm, A Stone-Weierstrass theorem for $ {C^\ast}$-algebras, Ann. of Math. (2) 72 (1960), 216-244. MR 22 #7005. MR 0116210 (22:7005)
  • [3] D. Voiculescu, A non-commutative Weyl-von Neumann theorem, Rev. Roumaine Math. Pures Appl. 21 (1976), 97-113. MR 0415338 (54:3427)
  • [4] I. M. Wils, Stone-Čech compactifications and representations of operator algebras, Doctoral dissertation, Catholic Univ. of Nijmegin, Nijmegin, 1968. MR 37 #4637. MR 0229059 (37:4637)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1977-0448090-1
Keywords: $ {C^\ast}$-algebra, state, pure state, vector state, Calkin algebra
Article copyright: © Copyright 1977 American Mathematical Society

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