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Central sequences associated with a state


Author: Sze Kai Tsui
Journal: Proc. Amer. Math. Soc. 82 (1981), 76-80
MSC: Primary 46L30
DOI: https://doi.org/10.1090/S0002-9939-1981-0603605-6
MathSciNet review: 603605
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Abstract: Central sequences associated with a state are defined and used to derive a characterization of the factor state in question. This characterization is used to study the factor state extension problem. One of the affirmative results obtained in this paper is as follows. Let $ \mathcal{A}_1$, be a finite dimensional sub-$ {C^ * }$*-algebra of $ \mathcal{A}$. Then every factor state on the relative commutant of $ \mathcal{A}_1$, in $ \mathcal{A}$ extends to a factor state on $ \mathcal{A}$.


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

  • [1] Charles Akemann and Gert Pedersen, Central sequences and inner derivations of separable $ {C^ * }$-algebras, preprint.
  • [2] Jacques Dixmier, Les $ {C^ * }$-algèbres et leurs representations, Gauthier-Villars, Paris, 1969. MR 0246136 (39:7442)
  • [3] George Elliott, Some $ {C^ * }$-algebras with outer derivations. III, Ann. of Math. (2) 106 (1977), 121-143. MR 0448093 (56:6403)
  • [4] Dusa McDuff, Central sequences and the hyperfinite factor, Proc. London Math. Soc. (3) 21 (1970), 443-461. MR 0281018 (43:6737)
  • [5] Shôichirô Sakai, On automorphism groups of $ {\text{I}}{{\text{I}}_1}$-factors, Tôhoku Math. J. (2) 26 (1974), 423-430. MR 0380443 (52:1343)
  • [6] -, $ {C^ * }$-algebras and $ {W^ * }$-algebras, Springer-Verlag, Berlin and New York, 1971.
  • [7] I. E. Segal, Irreducible representations of operator algebras, Bull. Amer. Math. Soc. 53 (1947), 73-88. MR 0020217 (8:520b)
  • [8] Jun Tomiyama, Tensor products and projections of norm one in von Neumann algebras, Seminar at Univ. of Copenhagen, 1970.
  • [9] Kôsaku Yosida, Functional analysis, 2nd ed., Die Grundlehren der Math. Wissenschaften, Bd. 123, Springer-Verlag, Berlin and New York, 1968. MR 0239384 (39:741)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0603605-6
Keywords: Central sequences associated with a state, factor states, Kaplansky's density theorem, factor state extension, extreme points, projection mapping of norm one
Article copyright: © Copyright 1981 American Mathematical Society

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