Tokyo Journal of Mathematics

The Countable Chain Condition for C*-Algebras

Shuhei MASUMOTO

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

In this paper, we introduce the countable chain condition for C*-algebras and study its fundamental properties. We show independence from $\mathsf{ZFC}$ of the statement that this condition is preserved under the tensor products of C*-algebras.

Article information

Source
Tokyo J. Math., Volume 38, Number 2 (2015), 513-522.

Dates
First available in Project Euclid: 14 January 2016

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1452806054

Digital Object Identifier
doi:10.3836/tjm/1452806054

Mathematical Reviews number (MathSciNet)
MR3448871

Zentralblatt MATH identifier
1373.46049

Subjects
Primary: 47L30: Abstract operator algebras on Hilbert spaces
Secondary: 03E35: Consistency and independence results 54A35: Consistency and independence results [See also 03E35]

Citation

MASUMOTO, Shuhei. The Countable Chain Condition for C*-Algebras. Tokyo J. Math. 38 (2015), no. 2, 513--522. doi:10.3836/tjm/1452806054. https://projecteuclid.org/euclid.tjm/1452806054


Export citation

References

  • E. Blanchard and E. Kirchberg, Non-simple purely infinite C*-algebras: the Hausdorff case, J. Funct. Anal. 207 (2004), no. 2, 461–513.
  • N. P. Brown and N. Ozawa, C*-algebras and finite-dimensional approximations, Graduate Studies in Mathematics, 88, American Mathematical Society, Providence, RI, 2008.
  • K. R. Davidson, C*-algebras by example, Fields Institute Monographs, 6, American Mathematical Society, Providence, RI, 1996.
  • T. Jech, Set theory, The third millenium edition, revised and expanded, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2003.
  • R. B. Jensen, The fine structure of the constructible hierarchy, With a section by Jack Silver, Ann. Math. Logic 4 (1972), 229-308; erratum, ibid. 4 (1972), 443.
  • K. Kunen, Set theory, An introduction to independence proofs, Studies in Logic and the Foundations of Mathematics, 102, North-Holland Publishing Co., Amsterdam-New York, 1980.
  • G. K. Pedersen, C*-algebras and their automorphism groups, London Mathematical Society Monographs, 14, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London-New York, 1979.
  • G. J. Murphy, C*-algebras and operator theory, Academic Press, Inc., Boston, MA, 1990.
  • M. Takesaki, Theory of operator algebras, I, Reprint of the first (1979) edition, Encyclopaedia of Mathematical Sciences, 124, Operator Algebras and Non-commutative Geometry, 5, Springer-Verlag, Berlin, 2002.
  • A. Wulfsohn, The primitive spectrum of a tensor product of C*-algebras, Proc. Amer. Math. Soc. 19 (1968), 1094–1096.