An example of a liminal $C^{\ast }$-algebra
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- by A. J. Lazar and D. C. Taylor PDF
- Proc. Amer. Math. Soc. 79 (1980), 50-54 Request permission
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
- Bruce E. Blackadar, Infinite tensor products of $C^*$-algebras, Pacific J. Math. 72 (1977), no. 2, 313–334. MR 512361, DOI 10.2140/pjm.1977.72.313
- Jacques Dixmier, Les $C^{\ast }$-algèbres et leurs représentations, Cahiers Scientifiques, Fasc. XXIX, Gauthier-Villars & Cie, Éditeur-Imprimeur, Paris, 1964 (French). MR 0171173 A. Wulfson, Produit tensoriel de ${C^ \ast }$-algèbres, Bull. Sci. Math. 87 (1963), 13-28.
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 79 (1980), 50-54
- MSC: Primary 46L05
- DOI: https://doi.org/10.1090/S0002-9939-1980-0560582-3
- MathSciNet review: 560582