Skip to main content
SpringerLink
Log in

Quasi-product states on C*-algebras

  • Conference paper
  • First Online:
Operator Algebras and their Connections with Topology and Ergodic Theory

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1132))

Abstract

We introduce and study a class of Markov measures, which we call quasi-product measures, on compact totally disconnected path spaces, and consider the induced states, called quasi-product states on the associated unital AF algebras and the infinite C*-algebras 0 A associated with a topological Markov chain A. For product spaces, and UHF algebras these are precisely product measures and product states respectively. In particular, we give sufficient conditions which ensure that the gauge group is weakly outer in certain quasi-product weights on the stablised C*-algebra of 0 A.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. H. Araki, A.L. Carey, D.E. Evans. On On+1. J. Operator Theory (in press).

    Google Scholar 

  2. H. Araki, R. Haag, D. Kastler, M. Takesaki. Extension of states and chemical potential. Commun. math. Phys. 53 (1977), 97–134.

    Article  MathSciNet  Google Scholar 

  3. O. Bratteli, D.W. Robinson, Operator Algebras and Quantum Statistical Mechanics II. Springer Verlag. Berlin, Heidelberg, New York 1981.

    Book  MATH  Google Scholar 

  4. J. Cuntz. Simple C*-algebras generated by isometries. Commun. math. Phys. 57 (1977), 173–185.

    Article  MathSciNet  MATH  Google Scholar 

  5. J. Cuntz, W. Krieger, A class of C*-algebras and topological Markov chains. Inventiones Math. 56 (1980), 251–258.

    Article  MathSciNet  MATH  Google Scholar 

  6. D.E. Evans. On On. Publ.RIMS Kyoto Univ. 16 (1980), 915–927.

    Article  MATH  Google Scholar 

  7. D.E. Evans. Entropy of automorphisms of AF algebras. Publ. RIMS Kyoto Univ. 18 (1982), 1045–1051.

    Article  MathSciNet  MATH  Google Scholar 

  8. D.E. Evans. The C*-algebras of topological Markov chains. Lecture notes. Tokyo Metropolitan University, 1983.

    Google Scholar 

  9. S. Kakutani. On equivalence of infinite product measures, Ann. of Math. 49 (1948), 214–222.

    Article  MathSciNet  MATH  Google Scholar 

  10. W. Krieger. On constructing non-isomorphic hyperfinite factors of type III. J. Func. Analysis. 6 (1970), 97–109.

    Article  MathSciNet  MATH  Google Scholar 

  11. C.C. Moore. Invariant measures on product spaces. Proc. of the Fifth Berkeley Symposium on Math. Stat. and Probability. Vol. II, part II, 447–459 (1967).

    MathSciNet  Google Scholar 

  12. E. Seneta. Non negative matrices and Markov chains. Springer-Verlag. Berlin, Heidelberg and New York. (2nd edition), 1981.

    Book  MATH  Google Scholar 

  13. S. Stratila, D. Voiculescu. Representations of AF algebras and of the group U(∞). Lecture notes in Mathematics. Springer-Verlag, vol. 486. Berlin, Heidelberg and New York, 1975.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematics Institute, University of Warwick, CV4 7AL, Coventry, England

    David E. Evans

Authors
  1. David E. Evans
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Huzihiro Araki Calvin C. Moore Åžerban-Valentin Stratila Dan-Virgil Voiculescu

Rights and permissions

Reprints and permissions

Copyright information

© 1985 Springer-Verleg

About this paper

Cite this paper

Evans, D.E. (1985). Quasi-product states on C*-algebras. In: Araki, H., Moore, C.C., Stratila, ÅžV., Voiculescu, DV. (eds) Operator Algebras and their Connections with Topology and Ergodic Theory. Lecture Notes in Mathematics, vol 1132. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074883

Download citation

  • DOI: https://doi.org/10.1007/BFb0074883

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15643-7

  • Online ISBN: 978-3-540-39514-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation