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

@article{J2008,
abstract = {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.},
author = {J. J. Grobler, H. Raubenheimer},
journal = {Studia Mathematica},
keywords = {trace; Fredholm element; index; socle; exponential spectrum},
language = {eng},
number = {3},
pages = {281-297},
title = {The index for Fredholm elements in a Banach algebra via a trace},
url = {http://eudml.org/doc/284665},
volume = {187},
year = {2008},
}

TY - JOUR
AU - J. J. Grobler
AU - H. Raubenheimer
TI - The index for Fredholm elements in a Banach algebra via a trace
JO - Studia Mathematica
PY - 2008
VL - 187
IS - 3
SP - 281
EP - 297
AB - 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.
LA - eng
KW - trace; Fredholm element; index; socle; exponential spectrum
UR - http://eudml.org/doc/284665
ER -