## Tokyo Journal of Mathematics

### The Countable Chain Condition for C*-Algebras

Shuhei MASUMOTO

#### 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

#### 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

#### 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.