Czechoslovak Mathematical Journal

, Volume 60, Issue 3, pp 589–596 | Cite as

On quasinilpotent equivalence of finite rank elements in Banach algebras



We characterize elements in a semisimple Banach algebra which are quasinilpotent equivalent to maximal finite rank elements.


maximal finite rank elements quasinilpotent equivalence 

MSC 2010

46H05 46H10 


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  1. [1]
    B. Aupetit, H. du T. Mouton: Trace and determinant in Banach algebras. Stud. Math. 121 (1996), 115–136.MATHMathSciNetGoogle Scholar
  2. [2]
    F.F. Bonsall, J. Duncan: Complete Normed Algebras. Springer, New York, 1973.MATHGoogle Scholar
  3. [3]
    I. Colojoarǎ, C. Foiǎs: Quasi-nilpotent equivalence of not necessarily commuting operators. J. Math. Mech. 15 (1966), 521–540.MathSciNetGoogle Scholar
  4. [4]
    I. Colojoarǎ and C. Foiǎs: Theory of generalized spectral operators. Mathematics and its Applications, vol. 9. Gordon and Breach, Science Publishers, New York-London-Paris, 1968.Google Scholar
  5. [5]
    L. Dalla, S. Giotopoulos, N. Katseli: The socle and finite-dimensionality of a semiprime Banach algebra. Stud. Math. 92 (1989), 201–204.MATHMathSciNetGoogle Scholar
  6. [6]
    C. Foiaš, F.-H. Vasilescu: On the spectral theory of commutators. J. Math. Anal. Appl. 31 (1970), 473–486.MATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    S. Giotopoulos, M. Roumeliotis: Algebraic ideals of semiprime Banach algebras. Glasgow Math. J. 33 (1991), 359–363.MATHCrossRefMathSciNetGoogle Scholar
  8. [8]
    R. Harte: On rank one elements. Stud. Math. 117 (1995), 73–77.MATHMathSciNetGoogle Scholar
  9. [9]
    S. Mouton, H. Raubenheimer: More spectral theory in ordered Banach algebras. Positivity 1 (1997), 305–317.MATHCrossRefMathSciNetGoogle Scholar
  10. [10]
    V. Müller: Spectral Theory of Linear Operators and Spectral Systems in Banach Algebras. Birkhäuser, Basel-Boston-Berlin, 2003.MATHGoogle Scholar
  11. [11]
    J. Puhl: The trace of finite and nuclear elements in Banach algebras. Czech. Math. J. 28 (1978), 656–676.MathSciNetGoogle Scholar
  12. [12]
    M. Razpet: The quasinilpotent equivalence in Banach algebras. J. Math. Anal. Appl. 166 (1992), 378–385.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Mathematical Institute, Academy of Sciences of Czech Republic 2010

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of JohannesburgAucklandparkSouth Africa

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