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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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


Author: Joel Anderson
Journal: Proc. Amer. Math. Soc. 65 (1977), 62-64
MSC: Primary 46L05
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] James Glimm, A Stone-Weierstrass theorem for 𝐶*-algebras, Ann. of Math. (2) 72 (1960), 216–244. MR 0116210
  • [3] Dan Voiculescu, A non-commutative Weyl-von Neumann theorem, Rev. Roumaine Math. Pures Appl. 21 (1976), no. 1, 97–113. MR 0415338
  • [4] W. I. M. Wils, Stone-Čech compactification and representations of operator algebras, Doctoral dissertation, Catholic University of Nijmegen, Faculteit der Wiskunde en Natuurwetenschappen aan de Katholieke Universiteit Nijmegen, Nijmegen, 1968 (English, with Dutch summary). MR 0229059

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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