The index for Fredholm elements in a Banach algebra via a trace
Tom 187 / 2008
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.
