Geodesic
Rank and the Drazin inverse in Banach algebras
R. M. Brits 1   ; L. Lindeboom 2   ; H. Raubenheimer 1
1 Department of Mathematics University of Johannesburg P.O. Box 524 Auckland Park 2006, South Africa
2 Department of Mathematics, Applied Mathematics and Astronomy University of South Africa P.O. Box 392 UNISA 0003, Pretoria, South Africa
Studia Mathematica, Tome 177 (2006) no. 3, pp. 211-224 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Let $A$ be an arbitrary, unital and semisimple Banach algebra with nonzero socle. We investigate the relationship between the spectral rank (defined by B. Aupetit and H. Mouton) and the Drazin index for elements belonging to the socle of $A$. In particular, we show that the results for the finite-dimensional case can be extended to the (infinite-dimensional) socle of $A$.
DOI : 10.4064/sm177-3-2
Mots-clés : arbitrary unital semisimple banach algebra nonzero socle investigate relationship between spectral rank defined aupetit mouton drazin index elements belonging socle particular results finite dimensional extended infinite dimensional socle

R. M. Brits  1   ; L. Lindeboom  2   ; H. Raubenheimer  1

1 Department of Mathematics University of Johannesburg P.O. Box 524 Auckland Park 2006, South Africa
2 Department of Mathematics, Applied Mathematics and Astronomy University of South Africa P.O. Box 392 UNISA 0003, Pretoria, South Africa 
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     title = {Rank and the {Drazin} inverse in {Banach} algebras},
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R. M. Brits; L. Lindeboom; H. Raubenheimer. Rank and the Drazin inverse in Banach algebras. Studia Mathematica, Tome 177 (2006) no. 3, pp. 211-224. doi: 10.4064/sm177-3-2

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