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

Abstract

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

This is a preview of subscription content, access via your institution.

References

  1. 1

    Arveson W.: Subalgebras of C*-algebras. Acta Math. 123, 141–224 (1969)

    MathSciNet  Article  MATH  Google Scholar 

  2. 2

    Arveson W.: Subalgebras of C*-algebras, II. Acta Math. 128, 271–308 (1972)

    MathSciNet  Article  MATH  Google Scholar 

  3. 3

    Arveson W.: The noncommutative Choquet boundary. J. Amer. Math. Soc. 21, 1065–1084 (2008)

    MathSciNet  Article  MATH  Google 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)

    MathSciNet  Article  MATH  Google 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)

    MathSciNet  MATH  Google 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)

  8. 8

    Davidson, K.R., Kennedy, M.: The Choquet boundary of an operator system. arXiv:1303.3252 preprint (2013)

  9. 9

    Farenick D.: Extremal matrix states on operator systems. J. Lond. Math. Soc. 61, 885–892 (2000)

    MathSciNet  Article  MATH  Google Scholar 

  10. 10

    Farenick D.: Pure matrix states on operator systems. Linear Algebra Appl. 393, 149–173 (2004)

    MathSciNet  Article  MATH  Google 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)

    MathSciNet  Article  MATH  Google Scholar 

  12. 12

    Hopenwasser A.: Boundary representations on C*-algebras with matrix units. Trans. Amer. Math. Soc. 177, 483–490 (1973)

    MathSciNet  MATH  Google Scholar 

  13. 13

    Morenz P.B.: The structure of C*-convex sets. Canad. J. Math. 46, 1007–1026 (1994)

    MathSciNet  Article  MATH  Google 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)

    MathSciNet  Article  MATH  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Douglas Farenick.

Additional information

In memory of William B. Arveson

This work is supported in part by the NSERC Discovery Grant program.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Argerami, M., Farenick, D. The C*-Envelope of an Irreducible Periodic Weighted Unilateral Shift. Integr. Equ. Oper. Theory 77, 199–210 (2013). https://doi.org/10.1007/s00020-013-2087-8

Download citation

Mathematics Subject Classification (2000)

  • Primary 46L07
  • Secondary 47A12
  • 47C10

Keywords

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