Integral Equations and Operator Theory

, Volume 77, Issue 2, pp 199–210 | Cite as

The C*-Envelope of an Irreducible Periodic Weighted Unilateral Shift

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Abstract

The C*-envelope of the 3-dimensional operator system generated by an irreducible periodic weighted unilateral shift operator is determined.

Mathematics Subject Classification (2000)

Primary 46L07 Secondary 47A12 47C10 

Keywords

C*-envelope boundary representation irreducible operator periodic weighted unilateral shift operator 
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References

  1. 1.
    Arveson W.: Subalgebras of C*-algebras. Acta Math. 123, 141–224 (1969)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Arveson W.: Subalgebras of C*-algebras, II. Acta Math. 128, 271–308 (1972)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Arveson W.: The noncommutative Choquet boundary. J. Amer. Math. Soc. 21, 1065–1084 (2008)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Bunce J., Salinas N.: Completely positive maps on C*-algebras and the left matricial spectra of an operator. Duke Math. J. 43, 747–774 (1976)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Bunce J.W., Deddens J.A.: Irreducible representations of the C*-algebra generated by an n-normal operator. Trans. Amer. Math. Soc. 171, 301–307 (1972)MathSciNetMATHGoogle Scholar
  6. 6.
    Bunce, J.W., Deddens, J.A.: C*-algebras generated by weighted shifts. Indiana Univ. Math. J. 23, 257–271 (1973/74)Google Scholar
  7. 7.
    Davidson, K.R.: C*-algebras by Example, volume 6 of Fields Institute Monographs. American Mathematical Society, Providence, RI (1996)Google Scholar
  8. 8.
    Davidson, K.R., Kennedy, M.: The Choquet boundary of an operator system. arXiv:1303.3252 preprint (2013)Google Scholar
  9. 9.
    Farenick D.: Extremal matrix states on operator systems. J. Lond. Math. Soc. 61, 885–892 (2000)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Farenick D.: Pure matrix states on operator systems. Linear Algebra Appl. 393, 149–173 (2004)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Farenick D., Gerasimova T.G., Shvai N.: A complete unitary similarity invariant for unicellular matrices. Linear Algebra Appl. 435, 409–419 (2011)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Hopenwasser A.: Boundary representations on C*-algebras with matrix units. Trans. Amer. Math. Soc. 177, 483–490 (1973)MathSciNetMATHGoogle Scholar
  13. 13.
    Morenz P.B.: The structure of C*-convex sets. Canad. J. Math. 46, 1007–1026 (1994)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Paulsen V.: Completely bounded maps and operator algebras, volume 78 of Cambridge Studies in advanced mathematics. Cambridge University Press, Cambridge (2002)Google Scholar
  15. 15.
    Tsai M.C., Wu P.Y.: Numerical ranges of weighted shift matrices. Linear Algebra Appl. 435, 243–254 (2011)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of ReginaReginaCanada

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