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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm187-3-5,
author = {J. J. Grobler and H. Raubenheimer},
title = {The index for Fredholm elements in a Banach algebra via a trace},
journal = {Studia Mathematica},
volume = {187},
year = {2008},
pages = {281-297},
zbl = {1166.46024},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm187-3-5}
}
J. J. Grobler; H. Raubenheimer. The index for Fredholm elements in a Banach algebra via a trace. Studia Mathematica, Tome 187 (2008) pp. 281-297. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm187-3-5/