Geodesic
The index for Fredholm elements in a Banach algebra via a trace
J. J. Grobler 1   ; H. Raubenheimer 2
1 Unit for Business Mathematics and Informatics North-West University Potchefstroom 2520, South Africa
2 Department of Mathematics University of Johannesburg Johannesburg 2006, South Africa
Studia Mathematica, Tome 187 (2008) no. 3, pp. 281-297 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

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.
DOI : 10.4064/sm187-3-5
Keywords: existence trace ideal banach algebra provides elegant develop abstract index theory fredholm elements algebra prove results problem equality nonzero exponential spectra elements and index theory formulate condition guaranteeing equality quotient algebra

J. J. Grobler  1   ; H. Raubenheimer  2

1 Unit for Business Mathematics and Informatics North-West University Potchefstroom 2520, South Africa
2 Department of Mathematics University of Johannesburg Johannesburg 2006, South Africa 
@article{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},
     pages = {281--297},
     year = {2008},
     volume = {187},
     number = {3},
     doi = {10.4064/sm187-3-5},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/sm187-3-5/}
}
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
SP  - 281
EP  - 297
VL  - 187
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4064/sm187-3-5/
DO  - 10.4064/sm187-3-5
LA  - en
ID  - 10_4064_sm187_3_5
ER  - 
%0 Journal Article
%A J. J. Grobler
%A H. Raubenheimer
%T The index for Fredholm elements
 in a Banach algebra via a trace
%J Studia Mathematica
%D 2008
%P 281-297
%V 187
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4064/sm187-3-5/
%R 10.4064/sm187-3-5
%G en
%F 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) no. 3, pp. 281-297. doi: 10.4064/sm187-3-5

Cité par Sources :