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An example of a liminal $ C\sp{\ast} $-algebra


Authors: A. J. Lazar and D. C. Taylor
Journal: Proc. Amer. Math. Soc. 79 (1980), 50-54
MSC: Primary 46L05
MathSciNet review: 560582
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Abstract: For each countable ordinal $ \gamma $ there exists a unital separable liminal $ {C^ \ast }$-algebra $ {A_\gamma }$ with the property that if $ ({I_\rho })_{\rho = 1}^\beta $ is any composition sequence of $ {A_\gamma }$ such that the spectra of the quotients $ {I_{\rho + 1}}/{I_\rho }$ are Hausdorff, then $ \beta \geqslant \gamma + 1$. Moreover, there is a composition sequence $ ({I_\rho })_{\rho = 1}^{\gamma + 1}$ of $ {A_\gamma }$ such that the spectra of the quotients $ {I_{\rho + 1}}/{I_\rho }$ are Hausdorff.


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

  • [1] Bruce E. Blackadar, Infinite tensor products of 𝐶*-algebras, Pacific J. Math. 72 (1977), no. 2, 313–334. MR 0512361
  • [2] Jacques Dixmier, Les 𝐶*-algèbres et leurs représentations, Cahiers Scientifiques, Fasc. XXIX, Gauthier-Villars & Cie, Éditeur-Imprimeur, Paris, 1964 (French). MR 0171173
  • [3] A. Wulfson, Produit tensoriel de $ {C^ \ast }$-algèbres, Bull. Sci. Math. 87 (1963), 13-28.

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DOI: https://doi.org/10.1090/S0002-9939-1980-0560582-3
Article copyright: © Copyright 1980 American Mathematical Society