Rank and the Drazin inverse in Banach algebras
Volume 177 / 2006
Studia Mathematica 177 (2006), 211-224
MSC: 46H05, 46H15, 47A99.
DOI: 10.4064/sm177-3-2
Abstract
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 $A$.
