Appendix to ``Regularity of Villadsen algebras'': The failure of the Corona Factorization Property for the Villadsen algebra $\mathcal{V}_\infty$

  • Joan Bosa
  • Martin S. Christensen

Abstract

In this appendix to M. S. Christensen, “Regularity of Villadsen algebras and characters on their central sequence algebras”, Math. Scand. ?? (????), ???--???, we prove that the Villadsen algebra $\mathcal{V} _\infty $ does not satisfy the Corona Factorization Property (CFP).

References

Blackadar, B., Robert, L., Tikuisis, A. P., Toms, A. S., and Winter, W., An algebraic approach to the radius of comparison, Trans. Amer. Math. Soc. 364 (2012), no. 7, 3657–3674. https://doi.org/10.1090/S0002-9947-2012-05538-3

Bosa, J. and Petzka, H., Comparison Properties of the Cuntz semigroup and applications to C*-algebras, Canad. J. Math. 70 (2018), no. 1, 26–52. https://doi.org/10.4153/CJM-2016-049-8

Goodearl, K. R., Riesz decomposition in inductive limit $C^*$-algebras, Rocky Mountain J. Math. 24 (1994), no. 4, 1405–1430. https://doi.org/10.1216/rmjm/1181072345

Kucerovsky, D. and Ng, P. W., A simple $C^ast $-algebra with perforation and the corona factorization property, J. Operator Theory 61 (2009), no. 2, 227–238.

Ortega, E., Perera, F., and Rørdam, M., The corona factorization property, stability, and the Cuntz semigroup of a $C^ast $-algebra, Int. Math. Res. Not. IMRN (2012), no. 1, 34–66. https://doi.org/10.1093/imrn/rnr013

>

Published
2018-08-06
How to Cite
Bosa, J., & Christensen, M. (2018). Appendix to ``Regularity of Villadsen algebras’’: The failure of the Corona Factorization Property for the Villadsen algebra $\mathcal{V}_\infty$. MATHEMATICA SCANDINAVICA, 123(1), 142-146. https://doi.org/10.7146/math.scand.a-104841
Section
Articles