Illinois Journal of Mathematics

Ultraproducts of crossed product von Neumann algebras

Reiji Tomatsu

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


We study a relationship between the ultraproduct of a crossed product von Neumann algebra and the crossed product of an ultraproduct von Neumann algebra. As an application, the continuous core of an ultraproduct von Neumann algebra is described.

Article information

Illinois J. Math., Volume 61, Number 3-4 (2017), 275-286.

Received: 17 May 2017
Revised: 23 January 2018
First available in Project Euclid: 22 August 2018

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46L10: General theory of von Neumann algebras
Secondary: 46L40: Automorphisms


Tomatsu, Reiji. Ultraproducts of crossed product von Neumann algebras. Illinois J. Math. 61 (2017), no. 3-4, 275--286. doi:10.1215/ijm/1534924828.

Export citation


  • H. Ando and U. Haagerup, Ultraproducts of von Neumann algebras, J. Funct. Anal. 266 (2014), 6842–6913.
  • C. Houdayer, A. Marrakchi and P. Verraedt, Fullness and Connes' $\tau$ invariant of type III tensor product factors, available at \arxivurlarXiv:1611.07914.
  • E. Kirchberg, Commutants of unitaries in UHF algebras and functorial properties of exactness, J. Reine Angew. Math. 452 (1994), 39–77.
  • A. Marrakchi, Spectral gap characterization of full type III factors, to appear in J. Reine Angew. Math.
  • T. Masuda and R. Tomatsu, Rohlin flows on von Neumann algebras, Mem. Amer. Math. Soc. 244 (2016), no. 1153, ix $+$ 111 pp.
  • T. Masuda and R. Tomatsu, Classification of actions of discrete Kac algebras on injective factors, Mem. Amer. Math. Soc. 245 (2017), no. 1160, ix $+$ 118 pp.
  • A. Ocneanu, Actions of discrete amenable groups on von Neumann algebras, Lecture Notes in Mathematics, vol. 1138, Springer-Verlag, Berlin, 1985.
  • Y. Raynaud, On ultrapowers of non commutative $L_p$ spaces, J. Operator Theory 48 (2002), no. 1, 41–68.
  • W. Rudin, Real and complex analysis, 3rd ed., McGraw-Hill, New York, 1987.
  • M. Takesaki, Conditional expectations in von Neumann algebras, J. Funct. Anal. 9 (1972), 306–321.
  • M. Takesaki, Theory of operator algebras. II, Encyclopaedia of Mathematical Sciences, vol. 125, Operator Algebras and Non-commutative Geometry, vol. 6, Springer-Verlag, Berlin, 2003.
  • R. Tomatsu and Y. Ueda, A characterization of fullness of continuous cores of type III$_1$ free product factors, Kyoto J. Math. 56 (2016), 599–610.