Skip to main content
Log in

Bipolar theorem for quantum cones

  • Brief Communications
  • Published:
Functional Analysis and Its Applications Aims and scope

Abstract

In this note duality properties of quantum cones are investigated. We propose a bipolar theorem for quantum cones, which provides a new proof of the operator bipolar theorem proved by Effros and Webster. In particular, a representation theorem for a quantum cone is proved.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. M. D. Choi and E. G. Effros, J. Funct. Anal., 24: 2 (1977), 156–209.

    Article  MathSciNet  MATH  Google Scholar 

  2. A. A. Dosiev, J. Funct. Anal., 255: 7 (2008), 1724–1760.

    Article  MathSciNet  MATH  Google Scholar 

  3. A. A. Dosiev, C. R. Math. Acad. Sci. Paris, 344: 10 (2007), 627–630.

    Article  MathSciNet  MATH  Google Scholar 

  4. A. A. Dosi, Trans. Amer. Math. Soc., 363: 2 (2011), 801–856.

    Article  MathSciNet  MATH  Google Scholar 

  5. A. A. Dosi, J. Math. Phys., 51: 6 (2010), 1–43.

    Article  MathSciNet  Google Scholar 

  6. A. A. Dosi, Inter. J. Math., 22: 4 (2011), 1–7.

    MathSciNet  Google Scholar 

  7. E. G. Effros and Z-.J. Ruan, Operator Spaces, Clarendon Press, Oxford, 2000.

    MATH  Google Scholar 

  8. E. G. Effros and C. Webster, in: Operator Algebras and Applications (Samos 1996), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., vol. 495, Kluwer Acad. Publ., Dordrecht, 1997, 163–207.

    Google Scholar 

  9. E. G. Effros and S. Winkler, J. Funct. Anal., 144: 1 (1997), 117–152.

    Article  MathSciNet  MATH  Google Scholar 

  10. A. Ya. Khelemskii, Quantum Functional Analysis, Amer. Math. Soc., Providence, RI, 2010.

    Google Scholar 

  11. S. S. Kutateladze, Fundamentals of Functional Analysis, Kluwer Texts in the Math. Sciences, vol. 12, Kluwer Acad. Publ., Dordrecht, 1996.

    Google Scholar 

  12. G. J. Murphy, C*-algebras and operator theory, Academic Press, Boston, MA, 1990.

    MATH  Google Scholar 

  13. V. Paulsen, Completely Bounded Maps and Operator Algebras, Cambridge Studies Advanced Math., vol. 78, Cambridge Univ. Press, Cambridge, 2002.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. Dosi.

Additional information

__________

Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 46, No. 3, pp. 84–89, 2012

Original Russian Text Copyright © by A. Dosi

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dosi, A. Bipolar theorem for quantum cones. Funct Anal Its Appl 46, 228–231 (2012). https://doi.org/10.1007/s10688-012-0029-x

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10688-012-0029-x

Key words

Navigation