Functional Analysis and Its Applications

, Volume 46, Issue 3, pp 228–231 | Cite as

Bipolar theorem for quantum cones

Brief Communications

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.

Key words

quantum cones absolutely matrix convex set quantum system 

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References

  1. [1]
    M. D. Choi and E. G. Effros, J. Funct. Anal., 24: 2 (1977), 156–209.MathSciNetMATHCrossRefGoogle Scholar
  2. [2]
    A. A. Dosiev, J. Funct. Anal., 255: 7 (2008), 1724–1760.MathSciNetMATHCrossRefGoogle Scholar
  3. [3]
    A. A. Dosiev, C. R. Math. Acad. Sci. Paris, 344: 10 (2007), 627–630.MathSciNetMATHCrossRefGoogle Scholar
  4. [4]
    A. A. Dosi, Trans. Amer. Math. Soc., 363: 2 (2011), 801–856.MathSciNetMATHCrossRefGoogle Scholar
  5. [5]
    A. A. Dosi, J. Math. Phys., 51: 6 (2010), 1–43.MathSciNetCrossRefGoogle Scholar
  6. [6]
    A. A. Dosi, Inter. J. Math., 22: 4 (2011), 1–7.MathSciNetGoogle Scholar
  7. [7]
    E. G. Effros and Z-.J. Ruan, Operator Spaces, Clarendon Press, Oxford, 2000.MATHGoogle Scholar
  8. [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. [9]
    E. G. Effros and S. Winkler, J. Funct. Anal., 144: 1 (1997), 117–152.MathSciNetMATHCrossRefGoogle Scholar
  10. [10]
    A. Ya. Khelemskii, Quantum Functional Analysis, Amer. Math. Soc., Providence, RI, 2010.Google Scholar
  11. [11]
    S. S. Kutateladze, Fundamentals of Functional Analysis, Kluwer Texts in the Math. Sciences, vol. 12, Kluwer Acad. Publ., Dordrecht, 1996.Google Scholar
  12. [12]
    G. J. Murphy, C*-algebras and operator theory, Academic Press, Boston, MA, 1990.MATHGoogle Scholar
  13. [13]
    V. Paulsen, Completely Bounded Maps and Operator Algebras, Cambridge Studies Advanced Math., vol. 78, Cambridge Univ. Press, Cambridge, 2002.Google Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Middle East Technical UniversityAnkaraTurkey

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