Universality of Some C*-Algebra Generated by a Unitary and a Self-adjoint Idempotent

  • Helena Mascarenhas
  • Bernd Silbermanna
Part of the Operator Theory: Advances and Applications book series (OT, volume 210)


We prove that there is essentially only one C *-algebra generated by a unitary element u and a self-adjoint idempotent p such that up=pup and up≠pu. This result is related to a theorem of L. Coburn stating that there is essentially only one C *-algebra generated by a non-unitary isometry.

Mathematics Subject Classification (2000)



C*-algebra finitely generated universality 


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  1. [1]
    L. COBURN: The C *-algebra generated by an isometry. Bull. Amer. Soc. 73 (1967), 722–726.zbMATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    I. GOHBERG, I. FELDMAN: Convolution Equations and Projection Methods for Their Solution. Nauka, Moskva 1971 (Russian) [Engl. translation: Transl. of Math. Monographs 41, Amer. Math. Soc., Providence, R.I., 1974].Google Scholar
  3. [3]
    S. PRÖSSDORF, B. SILBERMANN: Numerical Analysis for Integral and Related Operator Equations. Akademie-Verlag Berlin 1991, and Birkhäuser Verlag, Basel-Boston-Stuttgart, 1991.Google Scholar
  4. [4]
    V. OSTROVSKYI, Y. SAMOILENKO: Introduction to the theory of representations of finitely presented *-algebras. I. Representations by bounded operators, Harwood Academic Publishers, Amsterdam, 1999.Google Scholar
  5. [5] N. VASILEVSKII: C *-algebras generated by orthogonal projections and their applications. IEOT 31 (1998), no. 1, 113–132.MathSciNetGoogle Scholar

Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  • Helena Mascarenhas
    • 1
  • Bernd Silbermanna
    • 2
  1. 1.Instituto Superior TécnicoUniv. Técnica de LisboaLisbonPortugal
  2. 2.Technical University of ChemnitzFaculty of MathematicsChemnitzGermany

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