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

• Autorzy: J. J. Grobler , H. Raubenheimer
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46H10: Ideals and subalgebras
• 47A53: (Semi-) Fredholm operators; index theories
• 46H05: General theory of topological algebras
• 47A10: Spectrum, resolvent

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2008
• Tom: 187
• Numer: 3
• Strony: 281-297

Daty

wydano

2008

Twórcy

autor

J. J. Grobler

• Unit for Business Mathematics and Informatics, North-West University, Potchefstroom 2520, South Africa

autor

H. Raubenheimer

• Department of Mathematics, University of Johannesburg, Johannesburg 2006, South Africa

Identyfikatory

DOI

10.4064/sm187-3-5