Integral Equations and Operator Theory

, Volume 9, Issue 5, pp 739–743

A nil algebra of bounded operators on Hilbert space with semisimple norm closure

  • Donald Hadwin
  • Eric Nordgren
  • Mehdi Radjabalipour
  • Heydar Radjavi
  • Peter Rosenthal
Short Communications
  • 28 Downloads

Abstract

An algebra of operators having the property of the title is constructed and it is used to give examples related to some recent invariant subspace results.

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References

  1. 1.
    Dixon, P.G., A Jacobson-semisimple Banach algebra with a dense nil subalgebra, Coll. Math 37(1977), 81–82.Google Scholar
  2. 2.
    Grabiner, S., Nilpotents in Banach algebras, J. London Math. Soc. (2) 14(1976), 7–12.Google Scholar
  3. 3.
    Grabiner, S., The nilpotency of Banach algebras, Proc. Amer. Math. Soc. 21(1969), 510.Google Scholar
  4. 4.
    Hadwin, D.W., Nordgren, E.A., Radjabalipour, M., Radjavi, H. and Rosenthal, P., On simultaneous triangularization of collections of operators, to appear.Google Scholar
  5. 5.
    Kadison, R.V., and Ringrose, J.R., Foundations of the theory of operator algebras, Academic Press, New York, 1983.Google Scholar
  6. 6.
    Kaplansky, I., The Engel-Kolchin theorem revisited, in “Contributions to algebra”, Bass, Kovacik, Eds., Academic Press, New York, 1977, pp. 233–237.Google Scholar
  7. 7.
    Laurie, C., Nordgren, E., Radjavi, H. and Rosenthal, P., On triangularization of algebras of operators, J. reine angew. Math. 327(1981), 143–155.Google Scholar
  8. 8.
    Levitzki, J., Über nilpotente Unterringe, Math. Ann. 105(1931), 620–627.Google Scholar
  9. 9.
    Nordgren, E.A., Radjavi, H. and Rosenthal, P., Triangularizing semigroups of compact operators, Indiana Univ. Math. J. 33(1984), 271–275.Google Scholar
  10. 10.
    Radjavi, H., A trace condition equivalent to simultaneous triangularizability, Canad. J. Math., to appear.Google Scholar
  11. 11.
    Rickart, C.E., General theory of Banach algebras, Van Nostrand, Princeton, NJ, 1960.Google Scholar

Copyright information

© Birkhäuser Verlag 1986

Authors and Affiliations

  • Donald Hadwin
    • 1
  • Eric Nordgren
    • 1
  • Mehdi Radjabalipour
    • 3
  • Heydar Radjavi
    • 2
  • Peter Rosenthal
    • 4
  1. 1.Department of MathematicsUniversity of New HampshireDurham
  2. 2.Department of MathematicsDalhousie UniversityHalifaxCanada
  3. 3.Department of MathematicsKerman UniversityKermanIran
  4. 4.Department of MathematicsUniversity of TorontoTorontoCanada

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