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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On vector states and separable $C^*$-algebras
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by Joel Anderson PDF
Proc. Amer. Math. Soc. 65 (1977), 62-64 Request permission

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
    J. Anderson, Extreme points in sets of positive linear maps on $\mathcal {B}(\mathcal {H})$ (to appear).
  • James Glimm, A Stone-Weierstrass theorem for $C^{\ast }$-algebras, Ann. of Math. (2) 72 (1960), 216–244. MR 116210, DOI 10.2307/1970133
  • Dan Voiculescu, A non-commutative Weyl-von Neumann theorem, Rev. Roumaine Math. Pures Appl. 21 (1976), no. 1, 97–113. MR 415338
  • W. I. M. Wils, Stone-Čech compactification and representations of operator algebras, Katholieke Universiteit, Faculteit der Wiskunde en Natuurwetenschappen, Nijmegen, 1968 (English, with Dutch summary). Doctoral dissertation, Catholic University of Nijmegen. MR 0229059
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Additional Information
  • © Copyright 1977 American Mathematical Society
  • 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