The index for Fredholm elements in a Banach algebra via a trace

Tom 187 / 2008

J. J. Grobler, H. Raubenheimer Studia Mathematica 187 (2008), 281-297 MSC: Primary 46H05; Secondary 46H10, 47A10, 47A53. DOI: 10.4064/sm187-3-5

Streszczenie

We show that the existence of a trace on an ideal in a Banach algebra provides an elegant way to develop the abstract index theory of Fredholm elements in the algebra. We prove some results on the problem of the equality of the nonzero exponential spectra of elements $ab$ and $ba$ and use the index theory to formulate a condition guaranteeing this equality in a quotient algebra.

Autorzy

  • J. J. GroblerUnit for Business Mathematics and Informatics
    North-West University
    Potchefstroom 2520, South Africa
    e-mail
  • H. RaubenheimerDepartment of Mathematics
    University of Johannesburg
    Johannesburg 2006, South Africa
    e-mail

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